Question

Identify the matrix which represents the coordinates of ABC where A(-9, -6), B(-3, 3), and C(0, -3) after a dilation with a scale factor of 2/3

Answer 1

Given the coordinates of triangle ABC below;

`A(-9,-6),\text{ }B(-3,3)\text{ and }C(0,-3)`

For point matrix ABC, the formula is

`=\begin{bmatrix}{-9} & {-3} & {0} \\ {\placeholder{⬚}} & {\placeholder{⬚}} & {\placeholder{⬚}} \\ {-6} & {3} & {-3}\end{bmatrix}`

After dilation by a factor of 2/3, the matrix becomes

`\begin{gathered} =\begin{bmatrix}{(2)/(3)}\cdot-9 & {(2)/(3)}\cdot-3 & {(2)/(3)}\cdot0 \\ {\placeholder{⬚}} & {\placeholder{⬚}} & {\placeholder{⬚}} \\ {(2)/(3)}\cdot-6 & {(2)/(3)}\cdot3 & {(2)/(3)}\cdot-3\end{bmatrix} \\ =\begin{bmatrix}{-6} & {-2} & {0} \\ {\placeholder{⬚}} & {\placeholder{⬚}} & {\placeholder{⬚}} \\ {-4} & {2} & {-2}\end{bmatrix} \end{gathered}`

Hence, the answer is

`\begin{bmatrix}{-6} & {-2} & {0} \\ {\placeholder{⬚}} & {\placeholder{⬚}} & {\placeholder{⬚}} \\ {-4} & {2} & {-2}\end{bmatrix}`