Question

Work out the coordinate of R​

Answer 1

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

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((mx_2+nx_1)/(m+n),\:(my_2+ny_1)/(m+n)\bigg)`

• 
  `\implies R=\bigg((1(6)+3(-4))/(1+3),\:(1(11)+3(-1))/(1+3)\bigg)`

• 
  `\implies R=\bigg((6-12)/(4),\:(11-3)/(4)\bigg)`

• 
  `\implies R=\bigg((-6)/(4),\:(8)/(4)\bigg)`

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

Answer 2

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