# A triangle has corners at (1, 4 ), ( 2, 3 ), and ( 5 , 2 ). If the triangle is dilated by  3 x around (1, 1), what will the new coordinates of its corners be?

Feb 28, 2018

$\left(1 , 9 x + 1\right) , \left(3 x + 1 , 6 x + 1\right) , \left(12 x + 1 , 3 x + 1\right)$
Let's shift the expansion to be around the origin. Hence, the corners become $\left(0 , 3\right) , \left(1 , 2\right) , \left(4 , 1\right)$. We do this because expanding around the origin is really easy. We just multiply everything by that value.
Therefore, the expansion of these new points is $\left(0 , 9 x\right) , \left(3 x , 6 x\right) , \left(12 x , 3 x\right)$
$\left(1 , 9 x + 1\right) , \left(3 x + 1 , 6 x + 1\right) , \left(12 x + 1 , 3 x + 1\right)$