Question

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

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

\
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 the point \((-3,1)\)

For the point with \(x = - 3\) and \(y = 1\), using the formula \(x'=-y\) and \(y'=x\). Substitute \(y = 1\) into \(x'\): \(x'=-1\), substitute \(x=-3\) into \(y'\): \(y'=-3\).

Answer:

The value in the green box (corresponding to the \(x\) - coordinate of the rotated point of \((-3,1)\)) is \(-1\).