Given points, find the possible values of a

Question

Given the points A(a, 3), B(−2, 1) and C(3, 2), find the possible values of a if the length of AB is twice the length of BC.

Answer from textbook: a=-12 or a=8

Answer 1

Using the distance formula, we have:

 

√[(a-(-2))²+(3-1)²] = 2√[(-2-3)²+(1-2)²]

 

√(a²+4a+8) = 2√26

 

a²+4a+8 = 4(26)

 

a²+4a-96 = 0

 

(a+12)(a-8) = 0   a = -12 or a = 8