# Thread: Find the possible value for a.

1. ## Find the possible value for a.

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

2. using the distance formula to find the length of BC we have:

$\displaystyle \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$\displaystyle \sqrt{(5)^2+(1)^2$

$\displaystyle \sqrt{26}=BC$

using some algebra and the fact that AB will be twice BC:

$2\sqrt{26}=\sqrt{(a+2)^2+(2)^2}$

solve for a.

3. Thanks so much for all of your help.
I ended up getting a= -12 or 8, which is right. YAY!