Question

Let equations of line PQ, PR and QR are 2x - y -2 = 0, 4x + 3y = 24 and y + 4 = 0 respectively then find the length of perpendicular drawn from vertex P
on QR
Options
3
4
8
6​

Answer 1

Given :  equations of line PQ, PR and QR are 2x - y -2 = 0, 4x + 3y = 24 and y + 4 = 0 respectively

To Find : the length of perpendicular drawn from vertex P  on QR

Solution:

PQ  2x - y -2 = 0  => 4x - 2y  - 4  = 0

PR   4x + 3y = 24

P is intersection of PQ & PR

=>  5y + 4 = 24

=> 5y = 20

=> y = 4

 2x - y -2 = 0

=> 2x - 4 - 2 = 0

=> x = 4

P = (3 , 4)

y + 4 = 0   is  QR

y = - 4

Vertex P = ( 3 , 4)

length of perpendicular drawn from vertex P   on QR  ( 3, - 4)

= 4 -(-4)

= 8

8 is  the length of perpendicular drawn from vertex P  on QR

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