Question

rotate the given triangle 270° counterclockwise about the origin.
\\( \left \

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

\
ight \\)
\\( \left \

$$\begin{array} { c } { - 1 } \\\\ { 1 } \\end{array}$$

\
ight. \\) ? \\( \left. \

$$\begin{array} { c } { } \\\\ { } \\end{array}$$

\
ight \\)

Explanation:

Step1: Recall the rotation formula

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 formula to the second point

The second point of the original triangle is \((2,-1)\). Using the formula \((x = 2,y=-1)\), we get \(y=-1\) and \(-x=-2\).

Answer:

The value of the green - boxed element (the \(x\) - coordinate of the rotated second point) is \(-1\), and the value of the element below the green - boxed element (the \(y\) - coordinate of the rotated second point) is \(-2\).