CBSE Previous Year Question Paper
Class 10 Maths | 2018 Section B Question 10

Coordinate geometry question that appeared in section B of CBSE maths board paper in 2018. Solving the question requires knowledge of the section formula. Two parts to solving the question and both parts use the section formula.

Question 10: Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, - 3). Hence find m.

Video Explanation

Explanatory Answer

Let P (4, m) divide A (2, 3) and B (6, 3) in the ratio k : 1.
The x-coordinate of a point P that divides a line segment joining points A(x₁, y₁) and B(x₂, y₂) in the ratio k : 1 is \\frac{kx_{2} + x_{1}}{k + 1})

Part 1: Compute the ratio in which point P divides the line segment AB

Apply the section formula to the x-coordinate of point P
In this question, x₁= 2 and x₂ = 6
∴ \\frac{6k + 2}{k + 1}) = 4

6k + 2 = 4(k + 1)
6k + 2 = 4k + 4
2k = 2 or k = 1
If k = 1, p divides the segment AB in the ratio 1 : 1
So, p is the midpoint of AB.

Part 2: Compute the y-coordinate of point P to find the value of 'm'

Y coordinate of P = \\frac{y_{1} + y_{2}}{2}) = \\frac{3 - 3}{2}) = 0
m = 0