Question

For what value of x are the points A(-3, 12), B(7, 6) and C(x, 9) collinear.

Answer 1

A(-3,12) = (x1,y1)
B(7,6) = (x2,y2)
C(x,9) = (x3,y3)
As points A,B and C are collinear the area of triangle ABC is 0

$\frac{1}{2} |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)| = 0\\ = > \frac{1}{2} |( - 3)(6 - 9) + 7(9 - 12) + x(12 - 6)| = 0 \\ = > \frac{1}{2} |( - 3)( - 3) + 7( - 3) + x(6)| = 0 \\ = > \frac{1}{2} |9 + ( - 21) + 6x| = 0 \\ = > ( - 12) + 6x = 0 \\ = > 6x = 12 \\ = > x = \frac{12}{2} = 6$
Value of x is 6
I hope this helps

Answer 2

Answer:

the value of x is 2

Step-by-step explanation:

hope this helps :) ^_^