Question

dilate the given triangle by a magnitude of 3.
\\( \left \

$$\begin{array} { c c c } { 3 } & { 6 } & { 3 } \\\\ { - 3 } & { 3 } & { 3 } \\end{array}$$

\
ight \\)
\\( \left \

$$\begin{array} { c } { 9 } \\\\ { - 9 } \\end{array}$$

\
ight. \\)

Explanation:

Step1: Understand dilation rule

When dilating a matrix (representing coordinates) by a magnitude \(k\), each element is multiplied by \(k\). Here \(k = 3\).

Step2: Multiply the second - column element

The second - column element of the original matrix is \(6\) (in the first row) and \(3\) (in the second row).
For the first - row second - column: \(6\times3=18\)
For the second - row second - column: \(3\times3 = 9\)

Answer:

The matrix after dilation is \(

$$\begin{bmatrix}9&18&9\\- 9&9&9\end{bmatrix}$$

\), so the green box (first - row second - column) is \(18\) and the box below it (second - row second - column) is \(9\)