Coordinate Geometry | Class 10 Mathematics Notes

7.1 Introduction

Coordinate Geometry is a branch of mathematics that combines algebra and geometry to study geometric figures using algebraic methods. It is based on the idea of representing points on a plane using a pair of perpendicular coordinate axes, usually called the x-axis (horizontal) and y-axis (vertical). Each point on the plane is uniquely identified by an ordered pair of numbers (x, y), where x is the x-coordinate (or abscissa) representing the distance from the y-axis measured along the x-axis, and y is the y-coordinate (or ordinate) representing the distance from the x-axis measured along the y-axis. Points lying on the x-axis have coordinates of the form (x, 0), and points on the y-axis have coordinates of the form (0, y).

This chapter revisits these concepts and explores important topics such as finding the distance between two points, the midpoint of a line segment, the section formula, and the area of triangles using coordinates. It also connects algebraic equations to geometric representations, such as the fact that a linear equation in two variables represents a straight line on the coordinate plane. The chapter emphasizes the practical applications of coordinate geometry in fields like physics, engineering, navigation, seismology, and art.

An introductory activity invites students to plot given points on graph paper and join them in a specified order to form various geometric shapes, helping visualize the coordinate system and the connection between algebraic points and geometric figures.

📊 Diagram: 1062CH07

🧪 Activity: Plot the points A(4, 8), B(3, 9), C(3, 8), D(1, 6), E(1, 5), F(3, 3), G(6, 3), H(8, 5), I(8, 6), J(6, 8), K(6, 9), L(5, 8), and join them in the given order. Also, form triangles by joining points P(3.5, 7), Q(3, 6), R(4, 6), and similarly for other sets of points. Observe the geometric figures formed.

🔗 Connection: This introduction sets the stage for understanding the distance formula by explaining how points are represented on the coordinate plane, leading to the next section on calculating distances between points.