Question

rotate the given triangle 180° counterclockwise about the origin.
\

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

\

$$\begin{bmatrix} 0 & 3 & ? \\\\ 0 & & \\end{bmatrix}$$

Explanation:

Step1: Recall the rotation rule

When rotating a point \((x,y)\) \(180^{\circ}\) counter - clockwise about the origin, the new point is \((-x,-y)\).

Step2: Apply the rule to each point

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

Answer:

The matrix is \(

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

\)