# Coordinate Geometry

• Oct 19th 2010, 06:49 AM
Ilsa
Coordinate 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, 08:49 AM
Wilmer
What did you get? How did you get it?
• Oct 19th 2010, 08:53 AM
Ilsa
I used the distance formula but am not able to get the correct answer.
• Oct 19th 2010, 07:32 PM
Wilmer
Quote:

Originally Posted by Ilsa
I used the distance formula but am not able to get the correct answer.

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, 12:11 AM
mr fantastic
Quote:

Originally Posted by Ilsa
I used the distance formula but am not able to get the correct answer.

This reply sheds no light at all on what you did and why your answer might be wrong. How are we to know what mistake(s) you have made? Working that clearly shows how you got your answer is obviously needed!