Question

rotate the given triangle ( 270 ^ { circ } ) counterclockwise about the origin.
left \begin{array} { r r r } { - 1 } & { 2 } & { 2 } \\ { - 1 } & { - 1 } & { 3 } end{array}
ight
left \begin{array} { r r r } { - 1 } & { - 1 } & { 3 } \\ { 1 } & { - 2 } & {? } end{array}
ight

Explanation:

Step1: Recall the rotation rule

When rotating a point \((x,y)\) \(270^{\circ}\) counter - clockwise about the origin, the transformation rule is \((x,y)\to(y, - x)\).

Step2: Apply the rule to the third point

The original third point (from the first matrix) has \(x = 2\) and \(y=3\).
Using the rule \((x,y)\to(y, - x)\), we substitute \(x = 2\) and \(y = 3\) into the formula.
We get the new \(x\) - coordinate as \(y=3\) and the new \(y\) - coordinate as \(-x=- 2\).

Answer:

\(-2\)