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Fun GCSE Coordinate Geometry: Solved Questions and Cool PDFs!

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Studynotes_gcse

10/06/2022

Maths

Coordinate Geometry GCSE

Fun GCSE Coordinate Geometry: Solved Questions and Cool PDFs!

Coordinate Geometry in GCSE Mathematics: A Comprehensive Guide

This guide covers essential concepts in coordinate geometry for GCSE exams, including coordinates, gradients, midpoints, distance, straight lines, and perpendicular lines. It provides detailed explanations, formulas, and worked examples to help students master these topics.

...

10/06/2022

592

COORDINATE GEOMETRY
1- Coordinates
Two points (x₁, y₁) and (x₂, 1₂) es (-3.5) (2,8)
1₂ - Y₁ eig.
x₂-x,
1 GRADIENT = AY
Ax
Midpoint is the an

View

Drawing Graphs of Straight Lines

This section focuses on drawing graphs coordinate geometry GCSE questions and answers.

Methods for Drawing Straight Line Graphs

The page outlines different approaches to drawing straight line graphs:

  1. Using the y = mx + c form
  2. Plotting the y-intercept and using the gradient
  3. Finding x and y intercepts from the ax + by = c form

Example: A detailed worked example shows how to draw the lines y = 3x - 1 and 5x - 3y = 15 on the same set of axes.

The step-by-step process for plotting these lines is explained, including finding intercepts and using the gradient to plot additional points.

COORDINATE GEOMETRY
1- Coordinates
Two points (x₁, y₁) and (x₂, 1₂) es (-3.5) (2,8)
1₂ - Y₁ eig.
x₂-x,
1 GRADIENT = AY
Ax
Midpoint is the an

View

Perpendicular Lines

This page covers the concept of perpendicular lines in GCSE coordinate geometry questions and answers.

Understanding Perpendicular Lines

Definition: Perpendicular lines are lines that intersect at a right angle 90°90°.

The relationship between the gradients of perpendicular lines is explained:

Highlight: For two lines to be perpendicular, the product of their gradients must equal -1: m₁ × m₂ = -1.

Worked Example

The page includes a detailed worked example:

Example: Given a line with equation y = 2x + 2, find the equation of a perpendicular line passing through the point 2,32, -3.

The solution demonstrates how to:

  1. Find the perpendicular gradient
  2. Use the point-slope form to determine the equation
  3. Simplify to get the final answer: y = -½x - 2

This comprehensive guide provides students with the necessary tools to tackle GCSE coordinate geometry exam questions confidently.

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Maths

592

10 Jun 2022

3 pages

Fun GCSE Coordinate Geometry: Solved Questions and Cool PDFs!

Coordinate Geometry in GCSE Mathematics: A Comprehensive Guide

This guide covers essential concepts in coordinate geometry for GCSE exams, including coordinates, gradients, midpoints, distance, straight lines, and perpendicular lines. It provides detailed explanations, formulas, and worked examples to help... Show more

COORDINATE GEOMETRY
1- Coordinates
Two points (x₁, y₁) and (x₂, 1₂) es (-3.5) (2,8)
1₂ - Y₁ eig.
x₂-x,
1 GRADIENT = AY
Ax
Midpoint is the an

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Join milions of students

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Drawing Graphs of Straight Lines

This section focuses on drawing graphs coordinate geometry GCSE questions and answers.

Methods for Drawing Straight Line Graphs

The page outlines different approaches to drawing straight line graphs:

  1. Using the y = mx + c form
  2. Plotting the y-intercept and using the gradient
  3. Finding x and y intercepts from the ax + by = c form

Example: A detailed worked example shows how to draw the lines y = 3x - 1 and 5x - 3y = 15 on the same set of axes.

The step-by-step process for plotting these lines is explained, including finding intercepts and using the gradient to plot additional points.

COORDINATE GEOMETRY
1- Coordinates
Two points (x₁, y₁) and (x₂, 1₂) es (-3.5) (2,8)
1₂ - Y₁ eig.
x₂-x,
1 GRADIENT = AY
Ax
Midpoint is the an

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Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Perpendicular Lines

This page covers the concept of perpendicular lines in GCSE coordinate geometry questions and answers.

Understanding Perpendicular Lines

Definition: Perpendicular lines are lines that intersect at a right angle 90°90°.

The relationship between the gradients of perpendicular lines is explained:

Highlight: For two lines to be perpendicular, the product of their gradients must equal -1: m₁ × m₂ = -1.

Worked Example

The page includes a detailed worked example:

Example: Given a line with equation y = 2x + 2, find the equation of a perpendicular line passing through the point 2,32, -3.

The solution demonstrates how to:

  1. Find the perpendicular gradient
  2. Use the point-slope form to determine the equation
  3. Simplify to get the final answer: y = -½x - 2

This comprehensive guide provides students with the necessary tools to tackle GCSE coordinate geometry exam questions confidently.

COORDINATE GEOMETRY
1- Coordinates
Two points (x₁, y₁) and (x₂, 1₂) es (-3.5) (2,8)
1₂ - Y₁ eig.
x₂-x,
1 GRADIENT = AY
Ax
Midpoint is the an

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

Coordinates and Straight Lines

This page introduces fundamental concepts in coordinate geometry GCSE questions and answers.

Coordinates and Gradients

The page explains how to work with coordinates and calculate gradients between two points.

Definition: The gradient between two points x1,y1x₁, y₁ and x2,y2x₂, y₂ is calculated using the formula: y2y1y₂ - y₁ / x2x1x₂ - x₁.

Example: For points 3,5-3, 5 and 2,82, 8, the gradient would be 858 - 5 / 2(32 - (-3) = 3/5.

Midpoint and Distance

The concept of midpoint and distance between two points is introduced.

Highlight: The distance between two points is found using the Pythagorean theorem: √(x2x1)2+(y2y1)2(x₂ - x₁)² + (y₂ - y₁)².

Straight Line Equations

The page covers the general equation of a straight line: y = mx + c.

Vocabulary: In the equation y = mx + c, 'm' represents the gradient, and 'c' is the y-intercept.

A worked example demonstrates how to find the equation of a line parallel to y = 4x + 5 passing through the point 2,5-2, 5.

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Stefan S

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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