Question

P(–2, 5) and Q (3, 2) are two points. Find the coordinates of the point R on the line segment PQ such that PR = 2QR.

Answer 1

Given: P(–2, 5), Q(3, 2); find R on PQ with PR = 2 × QR. 

Step-wise calculation:

1. PR : QR = 2 : 1, so R divides PQ internally in the ratio 2 : 1 (m : n = 2 : 1).

2. Using the section formula

If PR : RQ = m : n, then `R = ((n xx x_1 + m xx x_2)/(m + n), (n xx y_1 + m xx y_2)/(m + n))` : 

`x_R = (1 xx (-2) + 2 xx 3)/(1 + 2)`

= `(-2 + 6)/3`

= `4/3` 

`y_R = (1 xx 5 + 2 xx 2)/(1 + 2)`

= `(5 + 4)/3`

= `9/3`

= 3

`R = (4/3, 3)`