Question

12. The line joining (-5, 7) and (0, -2) is perpendicular to the line joining (1. - 3) and (4,x) find x​

Answer 1

Answer:

The value of x = - 4/3

Step-by-step explanation:

Let A ( -5, 7) ,  B(0, -2)          

     C (1, -3) ,  D ( 4, x)

Slope m = $\frac{y_{2 - y_{1} } }{x_{2} - x_{1} }$

Slope of AB is m₁ = $\frac{ -2 - 7}{ 0 + 5}$  = -9/5

Slope of CD is m₂ = $\frac{x + 3}{4 - 1}$ = (x + 3)/3

Condition for perpendicularity is

m₁ x m₂ = -1

$\frac{(-9)}{5}$ x $\frac{(x+3)}{3}$  = - 1

- 3$x_{}$ - 9 = -5

3x = -9 + 5

  x = - 4/3