# A triangle has corners at (4, 5 ), ( 4, 3 ), and ( 4 , 2 ). If the triangle is dilated by  2 x around (1, 0), what will the new coordinates of its corners be?

Feb 12, 2018

New coordinates of the corners are color(blue)(A' (7,10), color(blue)(B' (7,6),color(blue)(C' (7,4)

#### Explanation:

Given : A (4,5), B (4,3), C(4,2)

Dilated about D(1,0) and dilation factor 2

To find the new coordinates of the corners

$\vec{A ' D} = 2 \cdot \vec{A D}$

$a ' - d = 2 \left(a - d\right)$ or $a ' = 2 a - d$

$\implies 2 \left(\begin{matrix}4 \\ 5\end{matrix}\right) - \left(\begin{matrix}1 \\ 0\end{matrix}\right) = \left(\begin{matrix}7 \\ 10\end{matrix}\right)$

color(blue)(A' (7,10)

$\vec{B ' D} = 2 \cdot \vec{B D}$

$b ' - d = 2 \left(b - d\right)$ or $b ' = 2 b - d$

$\implies 2 \left(\begin{matrix}4 \\ 3\end{matrix}\right) - \left(\begin{matrix}1 \\ 0\end{matrix}\right) = \left(\begin{matrix}7 \\ 6\end{matrix}\right)$

color(blue)(B' (7,6)

$\vec{C ' D} = 2 \cdot \vec{C D}$

$c ' - d = 2 \left(c - d\right)$ or $c ' = 2 c - d$

$\implies 2 \left(\begin{matrix}4 \\ 2\end{matrix}\right) - \left(\begin{matrix}1 \\ 0\end{matrix}\right) = \left(\begin{matrix}7 \\ 4\end{matrix}\right)$

color(blue)(C' (7,4)