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.
using the distance formula to find the length of BC we have:
$\displaystyle \displaystyle \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$
$\displaystyle \displaystyle \sqrt{(5)^2+(1)^2$
$\displaystyle \displaystyle \sqrt{26}=BC$
using some algebra and the fact that AB will be twice BC:
$\displaystyle 2\sqrt{26}=\sqrt{(a+2)^2+(2)^2}$
solve for a.