Question

write the coordinates of the vertices after a reflection over the line y = x.

Explanation:

Step1: Recall reflection rule

The rule for reflecting a point $(x,y)$ over the line $y = x$ is $(x,y)\to(y,x)$.

Step2: Identify original vertices

Assume the vertices are $N(0,0)$, $M(8,0)$, $L(8, - 10)$, $K(0,-10)$.

Step3: Apply reflection rule to $N$

For $N(0,0)$, after reflection, the new - coordinate is $(0,0)$ since $(0,0)\to(0,0)$ using the rule $(x,y)\to(y,x)$.

Step4: Apply reflection rule to $M$

For $M(8,0)$, after reflection, the new - coordinate is $(0,8)$ since $(8,0)\to(0,8)$ using the rule $(x,y)\to(y,x)$.

Step5: Apply reflection rule to $L$

For $L(8,-10)$, after reflection, the new - coordinate is $(-10,8)$ since $(8,-10)\to(-10,8)$ using the rule $(x,y)\to(y,x)$.

Step6: Apply reflection rule to $K$

For $K(0,-10)$, after reflection, the new - coordinate is $(-10,0)$ since $(0,-10)\to(-10,0)$ using the rule $(x,y)\to(y,x)$.

Answer:

The coordinates of the vertices $N$, $M$, $L$, $K$ after reflection over the line $y = x$ are $N(0,0)$, $M(0,8)$, $L(-10,8)$, $K(-10,0)$ respectively.