Question

P (-2,5) and Q (3, 2) are two points. Find the co-ordinates of the point Ron
PQ such that PR=2QR​

Answer 1

Given: Points P(-2, 5) and Q(3, 2).

To find: The coordinates of point R such that PR = 2QR.

Answer:

PQ is a line, and R is a point on PQ. According to the question, R divides PQ in the ratio 2:1.

Let the point on R be (x, y).

Section formula:

$\sf R(x,\ y)\ =\ \left(\dfrac{mx_2\ +\ nx_1}{m\ +\ n},\ \dfrac{my_2\ +\ ny_1}{m\ +\ n}\right)$

From the data we have,

• m = 2
• n = 1
• x₁ = -2
• x₂ = 3
• y₁ = 5
• y₂ = 2

Using them in the formula,

$\sf R(x,\ y)\ =\ \left(\dfrac{(2\ \times\ 3)\ +\ (1\ \times\ -2)}{2\ +\ 1},\ \dfrac{(2\ \times\ 2)\ +\ (1\ \times\ 5)}{2\ +\ 1}\right)\\\\\\R(x,\ y)\ =\ \left(\dfrac{6\ -\ 2}{3},\ \dfrac{4\ +\ 5}{3}\right)\\\\\\R(x,\ y)\ =\ \left(\dfrac{4}{3},\ \dfrac{9}{3}\right)\\\\\\R(x,\ y)\ =\ \left(\dfrac{4}{3},\ 3\right)$

Therefore, R divides the line PQ at R(4/3, 3) in the ratio 2:1.