•

10 Jan 2026

•

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... Show more

1 / 3

$# COORDINATE GEOMETPAY 1- Coordinares Two points $(x_1, y_1)$ and $(x_2, y_2)$ e.g. (-3.5) (2,8) 1 GRADIENT = $\frac{\Delta y}{\Delta x}$

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.

$# COORDINATE GEOMETPAY 1- Coordinares Two points $(x_1, y_1)$ and $(x_2, y_2)$ e.g. (-3.5) (2,8) 1 GRADIENT = $\frac{\Delta y}{\Delta x}$

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.

$# COORDINATE GEOMETPAY 1- Coordinares Two points $(x_1, y_1)$ and $(x_2, y_2)$ e.g. (-3.5) (2,8) 1 GRADIENT = $\frac{\Delta y}{\Delta x}$

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).

We thought you’d never ask...

What is the Knowunity AI companion?

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.

Where can I download the Knowunity app?

You can download the app from Google Play Store and Apple App Store.

Is Knowunity really free of charge?

That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.

Most popular content

An Inspector Calls: Character Insights

Explore in-depth analysis and key quotes for characters in J.B. Priestley's 'An Inspector Calls'. This resource covers Gerald Croft, Inspector Goole, Sheila Birling, Mrs. Birling, Eric Birling, and Eva Smith, focusing on themes of class, gender roles, and social responsibility. Ideal for students aiming for Grade 8 and above.

English Literature

aqa higher tier combined science - biology b1 : cell biology, paper 1

b1: cell biology - paper 1

Biology

Sociology of Families: Comprehensive Revision

Dive into an extensive overview of family dynamics, perspectives, and patterns in sociology. This resource covers key concepts such as family diversity, gender roles, marriage, and the impact of social policies on family structures. Perfect for A-Level Sociology students preparing for Paper 2.

Sociology

Comprehensive Crime & Deviance Overview

Explore an extensive revision of crime and deviance topics, including theories, types of crime, and the impact of media. This resource covers key concepts such as Marxism, functionalism, gender and crime, and the influence of globalization on criminal behavior. Ideal for students seeking a thorough understanding of criminology and its various theories. Type: Full Topic Revision.

Sociology

Sociology of Education Overview

Explore comprehensive A-Level Sociology notes on the education system, covering key theories, policies, and sociological perspectives. This resource includes insights on marketisation, gender roles, cultural deprivation, and educational inequalities, providing a thorough understanding of how education shapes social stratification and individual achievement. Ideal for exam preparation and in-depth study.

Sociology

Criminal Justice Evidence Rules

Explore the essential rules governing the use of evidence in criminal cases, including reliability, admissibility, and relevance. This summary covers key concepts such as the roles of personnel in investigations, the impact of witness testimonies, and the implications of plea bargaining. Ideal for Year 13 criminology students preparing for assessments.

Criminology

Macbeth: Guilt and Ambition

Explore the complex themes of guilt and ambition in Shakespeare's 'Macbeth'. This analysis covers key characters, including Macbeth and Lady Macbeth, their moral dilemmas, and the tragic consequences of their ambition. Ideal for students studying character motivations, thematic elements, and the psychological impact of power. Includes insights on the natural order, manipulation, and the descent into madness.

English Literature

Biology Paper 1 Overview

Comprehensive study notes covering key concepts in cellular biology, human digestion, respiration, photosynthesis, and the circulatory system. This resource includes detailed explanations of cell structures, enzyme functions, nutrient absorption, and the impact of environmental factors on biological processes. Ideal for students preparing for Biology Paper 1 exams.

Biology

Key Quotes from Macbeth

Explore essential quotes from Shakespeare's 'Macbeth' that highlight key themes such as ambition, guilt, and deception. This analysis includes significant lines from characters like Macbeth and Lady Macbeth, along with their context in the play. Ideal for students studying character development and thematic elements in literature.

English Literature

Can't find what you're looking for? Explore other subjects.

Students love us — and so will you.

4.9/5

App Store

4.8/5

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 Knowunity AI. 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

Stefan S

iOS user

Samantha Klich

Android user

Anna

iOS user

Best app on earth! no words because it’s too good

Thomas R

iOS user

Basil

Android user

David K

iOS user

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

Rohan U

Android user

Xander S

iOS user

Elisha

iOS user

Paul T

iOS user

Maths

•

604

•

10 Jan 2026

•

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. It provides detailed explanations, formulas, and worked examples to help... Show more

$# COORDINATE GEOMETPAY 1- Coordinares Two points $(x_1, y_1)$ and $(x_2, y_2)$ e.g. (-3.5) (2,8) 1 GRADIENT = $\frac{\Delta y}{\Delta x}$

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

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.

$# COORDINATE GEOMETPAY 1- Coordinares Two points $(x_1, y_1)$ and $(x_2, y_2)$ e.g. (-3.5) (2,8) 1 GRADIENT = $\frac{\Delta y}{\Delta x}$

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.

$# COORDINATE GEOMETPAY 1- Coordinares Two points $(x_1, y_1)$ and $(x_2, y_2)$ e.g. (-3.5) (2,8) 1 GRADIENT = $\frac{\Delta y}{\Delta x}$

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).