Question

rotate the given triangle 90° counterclockwise about the origin.
$\

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

$
$\

$$\begin{bmatrix} 0 & ? & \\\\ 0 & & \\end{bmatrix}$$

$

Explanation:

Step1: Recall rotation formula

When rotating a point \((x,y)\) \(90^{\circ}\) counter - clockwise about the origin, the transformation rule is \((x,y)\to(-y,x)\).

Step2: Apply the formula to the point \((-3,1)\)

For the point with \(x=-3\) and \(y = 1\), using the formula \((x,y)\to(-y,x)\), we substitute \(x=-3\) and \(y = 1\) into \(-y\) and \(x\). So, \(-y=-1\) and \(x=-3\) (wait, no, correction: the formula is \((x,y)\to(-y,x)\). For the point \((-3,1)\) (from the column \(

$$\begin{bmatrix}-3\\1\end{bmatrix}$$

\) in the original matrix), when we apply the rotation:
Let \(x=-3\) and \(y = 1\). The new \(x\) - coordinate is \(-y=-1\) and the new \(y\) - coordinate is \(x=-3\).

Answer:

\(

$$\begin{bmatrix}-1\\-3\end{bmatrix}$$

\)