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

Explanation:

Step1: Identify original vertices

Original coordinates: $A(-4, -10)$, $B(5, -10)$, $C(5, -5)$, $D(-4, -5)$

Step2: Apply reflection rule $y=-x$

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

• For $A(-4,-10)$: $(-(-10), -(-4))=(10, 4)$
• For $B(5,-10)$: $(-(-10), -(5))=(10, -5)$
• For $C(5,-5)$: $(-(-5), -(5))=(5, -5)$
• For $D(-4,-5)$: $(-(-5), -(-4))=(5, 4)$

Answer:

Reflected vertices: $A'(10, 4)$, $B'(10, -5)$, $C'(5, -5)$, $D'(5, 4)$