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How to Find Gradient, Midpoint Formula, and Solving Line Intersections Made Easy!

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E

Emily

25/03/2023

Maths

Further maths GCSE coordinate geometry

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How to Find Gradient, Midpoint Formula, and Solving Line Intersections Made Easy!

A comprehensive guide to coordinate geometry covering gradients, lines, and circles in mathematics. This guide explores essential concepts from GCSE to Further Mathematics level.

Key topics covered:

  • How to find gradient of a line using coordinates through various methods and formulas
  • Midpoint formula in coordinate geometry explained with practical examples
  • Solving intersection of two lines algebraically using simultaneous equations
  • Understanding circles, their equations, and tangent properties
  • Working with parallel and perpendicular lines
...

25/03/2023

574

co-ordinate geometry Gradient At GCSE: y = mx +C Ay AX EXI Find grad OF AB: A (2,1) Ex2 (814,7) P(3.1) (x, y) Distance between points Find d

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Page 2: Lines and Intersections

This page delves into equations of lines and their intersections, building upon the gradient concepts from the previous section.

Definition: The equation of a line can be expressed as y = mx + c GCSElevelGCSE level or y-y₁ = mx−x1x-x₁ point−slopeformpoint-slope form.

Example: Finding the equation of a line passing through −1,4-1,4 and 2,−32,-3 demonstrates practical application of line equations.

Highlight: Line intersections can be solved either algebraically using simultaneous equations or graphically by plotting.

Vocabulary: Y-intercept refers to the point where a line crosses the y-axis, represented by 'c' in y = mx + c.

co-ordinate geometry Gradient At GCSE: y = mx +C Ay AX EXI Find grad OF AB: A (2,1) Ex2 (814,7) P(3.1) (x, y) Distance between points Find d

View

Page 3: Circles and Tangents

This page explores circle equations and tangent properties, representing more advanced concepts in coordinate geometry.

Definition: The general equation of a circle with center a,ba,b is x−ax-a² + y−by-b² = r², where r is the radius.

Example: Finding the center and radius of x² - 2x + y² + 4y - 7 = 0 through completing the square method.

Highlight: Tangents are always perpendicular to the radius at the point of contact with the circle.

Vocabulary: Normal refers to a line perpendicular to a curve at a specific point, often used in context with tangents.

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Maths

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574

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25 Mar 2023

•

3 pages

How to Find Gradient, Midpoint Formula, and Solving Line Intersections Made Easy!

E

Emily

@emily_hoo

A comprehensive guide to coordinate geometry covering gradients, lines, and circles in mathematics. This guide explores essential concepts from GCSE to Further Mathematics level.

Key topics covered:

  • How to find gradient of a line using coordinatesthrough various methods and... Show more

co-ordinate geometry Gradient At GCSE: y = mx +C Ay AX EXI Find grad OF AB: A (2,1) Ex2 (814,7) P(3.1) (x, y) Distance between points Find d

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Page 2: Lines and Intersections

This page delves into equations of lines and their intersections, building upon the gradient concepts from the previous section.

Definition: The equation of a line can be expressed as y = mx + c GCSElevelGCSE level or y-y₁ = mx−x1x-x₁ point−slopeformpoint-slope form.

Example: Finding the equation of a line passing through −1,4-1,4 and 2,−32,-3 demonstrates practical application of line equations.

Highlight: Line intersections can be solved either algebraically using simultaneous equations or graphically by plotting.

Vocabulary: Y-intercept refers to the point where a line crosses the y-axis, represented by 'c' in y = mx + c.

co-ordinate geometry Gradient At GCSE: y = mx +C Ay AX EXI Find grad OF AB: A (2,1) Ex2 (814,7) P(3.1) (x, y) Distance between points Find d

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 3: Circles and Tangents

This page explores circle equations and tangent properties, representing more advanced concepts in coordinate geometry.

Definition: The general equation of a circle with center a,ba,b is x−ax-a² + y−by-b² = r², where r is the radius.

Example: Finding the center and radius of x² - 2x + y² + 4y - 7 = 0 through completing the square method.

Highlight: Tangents are always perpendicular to the radius at the point of contact with the circle.

Vocabulary: Normal refers to a line perpendicular to a curve at a specific point, often used in context with tangents.

co-ordinate geometry Gradient At GCSE: y = mx +C Ay AX EXI Find grad OF AB: A (2,1) Ex2 (814,7) P(3.1) (x, y) Distance between points Find d

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

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By signing up you accept Terms of Service and Privacy Policy

Page 1: Fundamentals of Coordinate Geometry

This page introduces core concepts of coordinate geometry, focusing on gradients and distances between points. The content progresses from basic GCSE concepts to more advanced applications.

Definition: Gradient is calculated using the formula y2−y1y₂-y₁/x2−x1x₂-x₁ where x1,y1x₁,y₁ and x2,y2x₂,y₂ are coordinates of two points on a line.

Example: Finding the gradient between points A2,12,1 and B4,74,7 demonstrates practical application of the gradient formula.

Highlight: Parallel lines have identical gradients M1=M2M₁ = M₂, while perpendicular lines have gradients that are negative reciprocals M1M2=−1M₁M₂ = -1.

Vocabulary: Modulus in coordinate geometry refers to the absolute value, ensuring only positive distances are considered.

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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

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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