Class 10 Maths Chapter 7, Coordinate Geometry, derives and applies the Distance Formula between two points (x1, y1) and (x2, y2) in the Cartesian plane and the Section Formula (including the Mid-point Formula) for internal division of a line segment in the ratio m1 : m2.
What Class 10 Mathematics (Ganit — Hindi Medium) Chapter 7 Covers
7.1 & 7.2 Distance Formula uses the Pythagoras theorem on right triangles in the coordinate plane to derive PQ = √((x2 – x1)2 + (y2 – y1)2) (and OP = √(x2 + y2) from the origin), applying it to test collinearity of three points, classify triangles (isosceles, equilateral, right-angled) and quadrilaterals (square, rhombus, rectangle, parallelogram), and find equidistant points on the x– or y-axis.
7.3 Section Formula uses similar right triangles to derive the coordinates of the point $P(x, y)$ dividing the line segment joining A(x1, y1) and B(x2, y2) internally in the ratio m1 : m2: P(x, y) = (m1x2 + m2x1 / m1 + m2, m1y2 + m2y1 / m1 + m2), with the special case $1:1$ giving the mid-point (x1 + x2 / 2, y1 + y2 / 2).
Exercises in Chapter 7
- Exercise 7.1 (10 Questions) covers distances between points, collinearity, Sports Day coordinate grid problems, identifying squares/parallelograms, and finding points on the axes equidistant from two given points.
- Exercise 7.2 (10 Questions) covers internal division ratios, points of trisection ($1:2$ and $2:1$), finding missing parallelogram vertices using mid-points of diagonals, and finding the area of a rhombus from its diagonals.
Read Class 10 Mathematics (Ganit — Hindi Medium) Chapter 7 Online
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FAQ
What is the Distance Formula in Class 10 Coordinate Geometry?
The distance between any two points P(x1, y1) and Q(x2, y2) is PQ = √((x2 – x1)2 + (y2 – y1)2). Its distance from the origin $(0,0)$ is √(x2 + y2).
What is the Section Formula for internal division in the ratio m1 : m2?
The coordinates of the point $P(x, y)$ dividing the segment joining A(x1, y1) and B(x2, y2) internally in the ratio m1 : m2 are (m1x2 + m2x1 / m1 + m2, m1y2 + m2y1 / m1 + m2).