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.

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- Oct 19th 2010, 07:49 AMIlsaCoordinate Geometry
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.

- Oct 19th 2010, 09:49 AMWilmer
What did you get? How did you get it?

- Oct 19th 2010, 09:53 AMIlsa
I used the distance formula but am not able to get the correct answer.

- Oct 19th 2010, 08:32 PMWilmer
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? - Oct 20th 2010, 01:11 AMmr fantastic