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4
0
Higher Maths Straight Line
118
•
1 Apr 2023
•
Emily Kelt
@emilykelt_yrng
This document covers key concepts in coordinate geometry, including collinearity,... Show more
This page delves into the properties of perpendicular lines and the methods for finding equations of straight lines.
Key concepts covered include:
Vocabulary: Perpendicular lines are lines that intersect at right angles .
Formula: The equation of a straight line formula is y = mx + c, where m is the gradient and c is the y-intercept.
Highlight: For perpendicular lines, the product of their gradients is always -1.
Example: Given points A and B, the gradient of line AB is calculated as m = )/ = 17.
The page also demonstrates how to find the equation of a line using the point-slope form: y - y₁ = m, where is a point on the line and m is the gradient.
Example: For line CD with gradient -1/3 passing through point D, the equation is derived as: y - 5 = -1/3, which simplifies to x + 3y - 16 = 0.
This page focuses on perpendicular bisectors and their applications in triangle geometry.
The main topics covered are:
Definition: A perpendicular bisector is a line that passes through the midpoint of a line segment at a right angle.
Example: To find the equation of perpendicular bisector of line AB where A and B, first calculate the midpoint , then use the perpendicular gradient to form the equation: y - 11 = -3/8.
Highlight: When dealing with vertical lines, the gradient is undefined, and the equation takes the form x = constant.
The page also introduces the concept of altitudes in triangles, which are perpendicular lines from a vertex to the opposite side.
Vocabulary: An altitude of a triangle is a line segment from a vertex perpendicular to the line containing the opposite side .
This page explores medians in triangles and various triangle centers.
Key concepts include:
Definition: A median is a line segment that connects a vertex to the midpoint of the opposite side in a triangle.
Example: In triangle ABC with A, B, and C, to find the equation of median BD, first calculate the midpoint of AC , then use the point-slope form with B to get the equation: 3y = 19x + 46.
Highlight: The centroid of a triangle is the point where all three medians intersect.
The page also mentions other important triangle centers:
This final page covers more complex problems involving lines and triangle centers.
Topics addressed include:
Example: To find the equation of a line AB making a 45° angle with the positive x-axis direction, use m = tan 45° = 1, resulting in the equation y = x - 3.
Highlight: The intersection point of perpendicular bisectors in a triangle is significant as it represents the circumcenter, which is equidistant from all three vertices.
The page concludes with a problem involving finding the intersection point of two lines, demonstrating the use of simultaneous equations to solve for the coordinates .
Vocabulary: The centroid of a triangle divides each median in the ratio 2:1, with the centroid being closer to the midpoint of the side.
This comprehensive guide provides a thorough understanding of how to find the equation of a straight line with one point, how to find midpoint coordinates on a graph, and various aspects of perpendicular bisector equations and calculations.
This page introduces fundamental concepts in coordinate geometry, including collinearity and distance between points.
The page covers:
Definition: Collinearity refers to points that lie on the same straight line.
Formula: The distance formula is used to calculate the length of a line segment: d = √
Example: For points A and B, the distance AB is calculated as √ = √ = √116 ≈ 10.77 units.
Highlight: The midpoint formula is crucial for finding the coordinates of the point exactly in the middle of a line segment: /2, /2
The page also touches on the concept of gradient and its relationship to the angle a line makes with the x-axis, introducing the formula m = tan θ.
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
App Store
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Emily Kelt
@emilykelt_yrng
This document covers key concepts in coordinate geometry, including collinearity, distance between points, midpoint formula, gradients, and equations of straight lines. It provides detailed explanations and examples for calculating distances, finding midpoints, determining gradients, and deriving line equations. The material... Show more
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page delves into the properties of perpendicular lines and the methods for finding equations of straight lines.
Key concepts covered include:
Vocabulary: Perpendicular lines are lines that intersect at right angles .
Formula: The equation of a straight line formula is y = mx + c, where m is the gradient and c is the y-intercept.
Highlight: For perpendicular lines, the product of their gradients is always -1.
Example: Given points A and B, the gradient of line AB is calculated as m = )/ = 17.
The page also demonstrates how to find the equation of a line using the point-slope form: y - y₁ = m, where is a point on the line and m is the gradient.
Example: For line CD with gradient -1/3 passing through point D, the equation is derived as: y - 5 = -1/3, which simplifies to x + 3y - 16 = 0.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page focuses on perpendicular bisectors and their applications in triangle geometry.
The main topics covered are:
Definition: A perpendicular bisector is a line that passes through the midpoint of a line segment at a right angle.
Example: To find the equation of perpendicular bisector of line AB where A and B, first calculate the midpoint , then use the perpendicular gradient to form the equation: y - 11 = -3/8.
Highlight: When dealing with vertical lines, the gradient is undefined, and the equation takes the form x = constant.
The page also introduces the concept of altitudes in triangles, which are perpendicular lines from a vertex to the opposite side.
Vocabulary: An altitude of a triangle is a line segment from a vertex perpendicular to the line containing the opposite side .
This page explores medians in triangles and various triangle centers.
Key concepts include:
Definition: A median is a line segment that connects a vertex to the midpoint of the opposite side in a triangle.
Example: In triangle ABC with A, B, and C, to find the equation of median BD, first calculate the midpoint of AC , then use the point-slope form with B to get the equation: 3y = 19x + 46.
Highlight: The centroid of a triangle is the point where all three medians intersect.
The page also mentions other important triangle centers:
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This final page covers more complex problems involving lines and triangle centers.
Topics addressed include:
Example: To find the equation of a line AB making a 45° angle with the positive x-axis direction, use m = tan 45° = 1, resulting in the equation y = x - 3.
Highlight: The intersection point of perpendicular bisectors in a triangle is significant as it represents the circumcenter, which is equidistant from all three vertices.
The page concludes with a problem involving finding the intersection point of two lines, demonstrating the use of simultaneous equations to solve for the coordinates .
Vocabulary: The centroid of a triangle divides each median in the ratio 2:1, with the centroid being closer to the midpoint of the side.
This comprehensive guide provides a thorough understanding of how to find the equation of a straight line with one point, how to find midpoint coordinates on a graph, and various aspects of perpendicular bisector equations and calculations.
This page introduces fundamental concepts in coordinate geometry, including collinearity and distance between points.
The page covers:
Definition: Collinearity refers to points that lie on the same straight line.
Formula: The distance formula is used to calculate the length of a line segment: d = √
Example: For points A and B, the distance AB is calculated as √ = √ = √116 ≈ 10.77 units.
Highlight: The midpoint formula is crucial for finding the coordinates of the point exactly in the middle of a line segment: /2, /2
The page also touches on the concept of gradient and its relationship to the angle a line makes with the x-axis, introducing the formula m = tan θ.
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
App Store
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
