Question

Work out the coordinate of R​

Answer 1

Answer:

The problem is with the arrangement of the ratios

PQ is the whole line but PR is a part of it only so you need QR to the ratio of PR

Answer 2

Answer:

$\huge{\red{ R=\bigg(-1.5,\: 2\bigg)}}$

Step-by-step explanation:

• Coordinates of the extreme points of the segment are P(-4, -1) and Q (6, 11)

• $\implies x_1= -4,\:y_1=-1,\:x_2=6,\:y_2=11$

• PQ = 4PR (Given)......(1)

• PQ = PR + RQ.....(2)

• -> 4PR = PR + RQ [From (1) and (2)]

• -> 4PR - PR = RQ

• -> 3PR = RQ

• -> PR/RQ = 1/3

• -> PR : RQ = 1 : 3

• This means point R divides segment PQ in the ratio 1 : 3.

• -> m : n = 1 : 3

• Now, coordinates of point R can be obtained by the section formula for internal division, which is given below:

• $R=\bigg(\frac{mx_2+nx_1}{m+n},\:\frac{my_2+ny_1}{m+n}\bigg)$

• $\implies R=\bigg(\frac{1(6)+3(-4)}{1+3},\:\frac{1(11)+3(-1)}{1+3}\bigg)$

• $\implies R=\bigg(\frac{6-12}{4},\:\frac{11-3}{4}\bigg)$

• $\implies R=\bigg(\frac{-6}{4},\:\frac{8}{4}\bigg)$

• $\implies\huge{\red{ R=\bigg(-1.5,\: 2\bigg)}}$