Question

rotate the given triangle 90° counterclockwise about the origin.
\\( \left \

$$\begin{array} { l l l } { 0 } & { - 3 } & { 5 } \\\\ { 0 } & { 1 } & { 2 } \\end{array}$$

\
ight \\)
\\( \left \

$$\begin{array} { l l l } { 0 } & { - 1 } & {? } \\\\ { 0 } & { } & { } \\end{array}$$

\
ight \\)

Explanation:

Step1: Recall rotation formula

When rotating a point \((x,y)\) \(90^{\circ}\) counter - clockwise about the origin, the new coordinates \((x',y')\) are given by \((x',y')=(-y,x)\).

Step2: Apply formula to each point

For the point \((- 3,1)\):
\(x=-3,y = 1\), then \(x'=-1,y'=-3\)
For the point \((5,2)\):
\(x = 5,y=2\), then \(x'=-2,y'=5\)

Answer:

\(

$$\begin{bmatrix}0&-1&-2\\0&-3&5\end{bmatrix}$$

\)