Given that the points A(a,a+1), B (-6, -3) and C (5,-1), find the possible values of a if the length of AB is twice the length of AC.
Well, let's see:
AB = SQT{[a - (-6)]^2 + [a+1 - (-3)]^2} = SQRT[(a + 6)^2 + (a + 4)^2]
AC = SQT{[a - 5]^2 + [a+1 - (-1)]^2} = SQRT[(a - 5)^2 + (a + 2)^2]
Since AB = twice AC:
SQRT[(a + 6)^2 + (a + 4)^2] = 2SQRT[(a - 5)^2 + (a + 2)^2]
Square both sides:
(a + 6)^2 + (a + 4)^2 = 4[(a - 5)^2 + (a + 2)^2]
Did you follow that? Can you wrap it up?