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Work out the coordinate of R​

Work Out The Coordinate Of R class=

Sagot :

mohammedtaisiralam06

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

View image mohammedtaisiralam06
Hrishii

Answer:

[tex]\huge{\red{ R=\bigg(-1.5,\: 2\bigg)}}[/tex]

Step-by-step explanation:

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

  • [tex]\implies x_1= -4,\:y_1=-1,\:x_2=6,\:y_2=11[/tex]

  • 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:

  • [tex]R=\bigg(\frac{mx_2+nx_1}{m+n},\:\frac{my_2+ny_1}{m+n}\bigg)[/tex]

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

  • [tex]\implies R=\bigg(\frac{6-12}{4},\:\frac{11-3}{4}\bigg)[/tex]

  • [tex]\implies R=\bigg(\frac{-6}{4},\:\frac{8}{4}\bigg)[/tex]

  • [tex]\implies\huge{\red{ R=\bigg(-1.5,\: 2\bigg)}}[/tex]
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