Question

7. The line passing through (-4, -2) and (2, -3)
is perpendicular to the line passing through
(a, 5) and (2, -1). Find a.​

Answer 1

ANSWER :–

a = 3

EXPLANATION :–

GIVEN :–

• A line passing through (-4, -2) and (2, -3) is perpendicular to the line passing through (a, 5) and (2, -1).

TO FIND :–

Value of 'a'

SOLUTION :–

☞ Slope of a line which is passing from (m,n) and (x,y) is –

=> $\\ \\ {\bold{\boxed{slope = \frac{y - n}{x - m} }}}$

• Slope of the which is passing from (-4, -2) and (2, -3) is –

=> $\\ \\ {slope = \frac{-3 - (-2)}{2 - ( -4) } }$

=> $m_{1} = - \frac{1}{6}$

• Slope of the which is passing from (a, 5) and (2, -1) is –

=> $\\ \\ {slope = \frac{-1 - 5}{2 - a} }$

=> $m_{2} = - \frac{6}{2-a}$

☞ According to question , both lines are perpendicular.

So that –

=> $\\ m_{1} \times m_{2}= - 1$

=> $\\ (- \frac{1}{6}) \times (- \frac{6}{2-a} ) = -1$

=> 1 = (-1)(2-a)

=> a - 2 = 1

=> a = 3