Fun GCSE Coordinate Geometry: Solved Questions and Cool PDFs!

Studynotes_gcse

12/10/2025

Maths

Coordinate Geometry GCSE

Subjects

Maths

Algebra

Straight line graphs

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12 Oct 2025

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3 pages

Fun GCSE Coordinate Geometry: Solved Questions and Cool PDFs!

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Coordinate Geometry in GCSE Mathematics: A Comprehensive Guide

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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

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:

Using the y = mx + c form
Plotting the y-intercept and using the gradient
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.

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°).

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 $2, -3$ .

The solution demonstrates how to:

Find the perpendicular gradient
Use the point-slope form to determine the equation
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.

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 $x₁, y₁$ and $x₂, y₂$ is calculated using the formula: $y₂ - y₁$ / $x₂ - x₁$ .

Example: For points $-3, 5$ and $2, 8$ , the gradient would be $8 - 5$ / $2 - (-3$ ) = 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: √ $(x₂ - x₁)² + (y₂ - y₁)²$ .

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 $-2, 5$ .

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Subjects

Maths

Algebra

Straight line graphs

Maths

12 Oct 2025

597

3 pages

Fun GCSE Coordinate Geometry: Solved Questions and Cool PDFs!

Studynotes_gcse @studynotes_gcse

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.... Show more

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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

Using the y = mx + c form
Plotting the y-intercept and using the gradient
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.

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

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°).

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 $2, -3$ .

The solution demonstrates how to

Find the perpendicular gradient
Use the point-slope form to determine the equation
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.

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 $x₁, y₁$ and $x₂, y₂$ is calculated using the formula $y₂ - y₁$ / $x₂ - x₁$ .

Example For points $-3, 5$ and $2, 8$ , the gradient would be $8 - 5$ / $2 - (-3$ ) = 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 √ $(x₂ - x₁)² + (y₂ - y₁)²$ .

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 $-2, 5$ .