Question

graph the image of rectangle abcd 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 $A(-10,-4)$, $B(-4,-4)$, $C(-4,5)$, $D(-10,5)$.

Step3: Apply reflection rule to $A$

For $A(-10,-4)$, after reflection, $A'(10,-4)$ since $x=- 10$ becomes $-x = 10$ and $y=-4$ remains the same.

Step4: Apply reflection rule to $B$

For $B(-4,-4)$, after reflection, $B'(4,-4)$ as $x = - 4$ becomes $-x=4$ and $y=-4$ is unchanged.

Step5: Apply reflection rule to $C$

For $C(-4,5)$, after reflection, $C'(4,5)$ because $x=-4$ turns to $-x = 4$ and $y = 5$ stays the same.

Step6: Apply reflection rule to $D$

For $D(-10,5)$, after reflection, $D'(10,5)$ since $x=-10$ changes to $-x = 10$ and $y = 5$ is constant.

Step7: Graph new rectangle

Plot points $A'(10,-4)$, $B'(4,-4)$, $C'(4,5)$, $D'(10,5)$ and connect them to form the reflected rectangle.

Answer:

Graph the rectangle with vertices $A'(10,-4)$, $B'(4,-4)$, $C'(4,5)$, $D'(10,5)$