# Coordinate Geometry

## Overview

Welcome to the exciting world of Coordinate Geometry! In this course material, we will delve into the fundamental concepts and tools required to understand and work with points, lines, and shapes on the Cartesian plane. The X-Y plane, also known as the Cartesian plane, is a two-dimensional plane formed by two number lines intersecting at a right angle. The horizontal line is the X-axis, while the vertical line is the Y-axis.

Concept Of The X-Y Plane: Understanding the X-Y plane is crucial as it provides a systematic way to represent and analyze geometric figures. The X-axis represents the horizontal direction, with positive values to the right of the origin and negative values to the left. Similarly, the Y-axis represents the vertical direction, with positive values above the origin and negative values below.

Coordinates Of Points On The X-Y Plane: Every point on the X-Y plane can be uniquely identified by an ordered pair of numbers (x, y), where 'x' represents the distance from the Y-axis (horizontal position) and 'y' represents the distance from the X-axis (vertical position). These coordinates allow us to precisely locate and describe the position of any point on the plane.

Calculate The Midpoint Of Two Points On The X-Y Plane: The midpoint between two points (x1, y1) and (x2, y2) is the point that lies exactly halfway between them. To calculate the midpoint coordinates, we average the x-coordinates to find the x-coordinate of the midpoint and average the y-coordinates to find the y-coordinate of the midpoint. This concept is essential in various applications, such as geometry and physics.

Calculate The Distance Between Two Points On The X-Y Plane: The distance between two points can be determined using the distance formula, which is derived from the Pythagorean theorem. By finding the horizontal and vertical differences between the points, we can form a right-angled triangle, and the hypotenuse of this triangle represents the distance between the two points. This calculation is invaluable in measuring lengths, finding perimeters, and solving real-life problems.

By mastering the topics covered in this course material, you will gain a solid foundation in Coordinate Geometry that is essential for advanced mathematical studies and practical applications. Get ready to explore the beauty and precision of working with points and shapes in the X-Y plane!

## Objectives

1. Understand the concept of the X-Y plane
2. Identify and plot coordinates of points on the X-Y plane
3. Calculate the distance between two points on the X-Y plane
4. Calculate the midpoint of two points on the X-Y plane

## Lesson Note

Coordinate Geometry, also known as Analytic Geometry, is a branch of geometry that defines and represents geometrical shapes using a coordinate system. The most commonly used coordinate system is the Cartesian coordinate system, which involves an X-Y plane.

## Lesson Evaluation

Congratulations on completing the lesson on Coordinate Geometry. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.

You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.

Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.

1. What are the coordinates of the point P(3, 5) on the X-Y plane? A. (3, 5) B. (5, 3) C. (5, 3) D. (3, 3) Answer: A. (3, 5)
2. Calculate the midpoint of the points A(2, 4) and B(6, 8) on the X-Y plane. A. (4, 6) B. (5, 7) C. (6, 8) D. (8, 4) Answer: A. (4, 6)
3. What is the distance between the points C(1, 2) and D(4, 6) on the X-Y plane? A. 5 units B. 6 units C. 7 units D. 8 units Answer: A. 5 units
4. If the point E lies on the X-axis, what can you say about its y-coordinate? A. y-coordinate is 0 B. y-coordinate is 1 C. y-coordinate is not defined D. y-coordinate is infinity Answer: A. y-coordinate is 0
6. If a point G lies on the line y = x, what can you say about its coordinates? A. x-coordinate = y-coordinate B. x-coordinate is negative C. y-coordinate is negative D. x-coordinate is 0 Answer: A. x-coordinate = y-coordinate
7. What is the equation of the X-axis in the X-Y plane? A. y = -x B. y = 0 C. x = 0 D. y = 1 Answer: B. y = 0
9. If a point J(5, 0) lies on the X-axis, what can you say about its x-coordinate? A. x-coordinate is 0 B. x-coordinate is positive C. x-coordinate is negative D. x-coordinate is 5 Answer: D. x-coordinate is 5
10. What are the coordinates of the origin on the X-Y plane? A. (1, 1) B. (-1, -1) C. (0, 0) D. (0, 1) Answer: C. (0, 0)

## Past Questions

Wondering what past questions for this topic looks like? Here are a number of questions about Coordinate Geometry from previous years

Question 1

A ship sets sail from port A (86o N, 56o W) for port B (86o N, 64o W), which is close by. Find the distance the ship covered from port A to port B, correct to the nearest km.

[Take π = 3.142 and R = 6370 km]

Question 1

In the diagram above, PQ and XY are two concentric arc; center O, the ratio of the length of the two arc is 1:3, find the ratio of the areas of the two sectors OPQ and OXY

Question 1

Two ladders of length 5m and 7m lean against a pole and make angles 45° and 60° with the ground respectively. What is their distance apart on the pole correct to two decimal places?

Practice a number of Coordinate Geometry past questions