P lies on the line 8y –15x = 0 and Q lies on the line 10y –... | MATH - ANGLE BETWEEN TWO STRAIGHT LINES | SolveeIt | Solveeit

Today, August 19

Question

P lies on the line 8y –15x = 0 and Q lies on the line

10y –3x = 0 and the mid-point of PQ is (8, 6). The distance PQ is-

A

$\frac { 50 } { 7 }$

B

$\frac { 60 } { 7 }$

C

$\frac { 50 } { 3 }$

D

$\frac { 60 } { 3 }$

Answer

$\frac { 60 } { 7 }$

Explanation

Solution

The line through (8, 6) and parallel to OQ is

10y = 3x + 36 and thus meets OP at $\left( \frac { 16 } { 7 } , \frac { 30 } { 7 } \right)$ . But this is mid-point of OP. So P is $\left( \frac { 32 } { 7 } , \frac { 60 } { 7 } \right)$