Question

The three points (3, -5) , (-a+2,3) and (2a+3, 2) lie on the same line. what is a?

Answer 1

Answer:

a = -7/23.

Step-by-step explanation:

For them to lie on the same line the slope of the line joining the first 2 points must equal the slope of the line joining the second and third points.

so (3 - -5) / (-a+2 - 3) =   (2 - 3) /[(2a + 3) - (-a + 2)]

8 / (-a - 1) = -1 /  (3a + 1)    Cross multiply:

-1(-a - 1) = 8(3a + 1)

a + 1 = 24a + 8

-7 = 23a

a = -7/23.