Suppose A, B are two pointegrals on 2x – y + 3 = 0 and P(1,... | MATH - ANGLE BETWEEN TWO STRAIGHT LINES | SolveeIt | Solveeit

Today, August 18

Question

Suppose A, B are two points on 2x – y + 3 = 0 and P(1, 2) is such that PA = PB. Then the mid-point of AB is –

A

$\left( - \frac { 1 } { 5 } , \frac { 13 } { 5 } \right)$

B

$\left( \frac { - 7 } { 5 } , \frac { 9 } { 5 } \right)$

C

$\left( \frac { 7 } { 5 } , \frac { - 9 } { 5 } \right)$

D

$\left( \frac { - 7 } { 5 } , \frac { - 9 } { 5 } \right)$

Answer

$\left( - \frac { 1 } { 5 } , \frac { 13 } { 5 } \right)$

Explanation

Solution

Equation of AB = 2x – y + 3 = 0

Ž D PAD $\cong$ D PBD

Ž D is Foot of perpendicular Ž from P to AB

$\frac { \alpha - 1 } { 2 }$ = $\frac { - ( 2 \times 1 - 1 \times 2 + 3 ) } { 4 + 1 }$

$\frac { \beta - 2 } { - 1 }$ = $\frac { 13 } { 5 }$