Question

write the coordinates of the vertices after a reflection over the y - axis.

Explanation:

Step1: Recall reflection rule

The rule for reflecting a point $(x,y)$ over the $y -$axis is $(-x,y)$.

Step2: Identify original vertices

Assume the vertices of the rectangle are $A(- 10,-10)$, $B(0,-10)$, $C(0,0)$, $D(-10,0)$.

Step3: Apply reflection rule to each vertex

For vertex $A(-10,-10)$: After reflection over the $y -$axis, the new coordinates are $(10,-10)$ using the rule $(-x,y)$.
For vertex $B(0,-10)$: After reflection over the $y -$axis, the new coordinates are $(0,-10)$ since $-0 = 0$.
For vertex $C(0,0)$: After reflection over the $y -$axis, the new coordinates are $(0,0)$.
For vertex $D(-10,0)$: After reflection over the $y -$axis, the new coordinates are $(10,0)$.

Answer:

The new vertices are $A(10,-10)$, $B(0,-10)$, $C(0,0)$, $D(10,0)$