Question

(Need solution fast) step by step please
The coordinates of three points A(-1,-6), B(3,-12) and C(k,6). Find the value of k if AB is perpendicular to AC.

Answer 1

Answer:

$k = 17$

Step-by-step explanation:

A(-1,-6); B(3, -12) and C(k,6)

We know that, the product of the slopes of Perpendicular Lines is -1.

Slope of Line AB $=\frac{difference between Ordinates}{difference between Abscissas}$ $=\frac{-6 - (-12)}{- 1 - 3} = \frac{6}{-4} =-\frac{3}{2}$

Slope of Line AC $=\frac{difference between Ordinates}{difference between Abscissas}$ $=\frac{-6 - 6}{- 1 - k} = \frac{12}{1+k}$

Since, AB is perpendicular to AC,

∴ $-\frac{3}{2} . \frac{12}{1+k} = -1$

$=> 1 + k = 18$

$=> k = 17$