Question

reflect the given triangle over the line y = x.
\\( \left \

$$\begin{array} { c c c } { 3 } & { 6 } & { 3 } \\\\ { - 3 } & { 3 } & { 3 } \\end{array}$$

\
ight \\)
\\( \left \

$$\begin{array} { c } { - 3 } \\\\ { 3 } \\end{array}$$

\
ight. \\)

Explanation:

Step1: Recall reflection over \(y = x\) rule

When reflecting a point \((x,y)\) over the line \(y=x\), the transformation is \((x,y)\to(y,x)\).

Step2: Apply the rule to the second - point

The original second - point of the triangle has coordinates \((x = 6,y = 3)\). After reflection over \(y=x\), using the rule \((x,y)\to(y,x)\), we get \((3,6)\).

Answer:

The value in the green box is \(3\) and the value in the box below the green box is \(6\). The completed matrix for the reflected triangle (assuming the order of points is maintained) will have the second - column entries \(3\) (top) and \(6\) (bottom).