Question

a line segment has endpoints at (-4,-6) and (-6,4). which reflection will produce an image with endpoints at (4,-6) and (6,4)? a reflection of the line segment across the y - axis a reflection of the line segment across the line y = x a reflection of the line segment across the line y = -x a reflection of the line segment across the x - axis

Explanation:

Step1: Recall reflection rules

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

Step2: Apply the rule to endpoints

For the point $(-4,-6)$, when reflected across the $y -$axis, we get $(-(-4),-6)=(4,-6)$. For the point $(-6,4)$, when reflected across the $y -$axis, we get $(-(-6),4)=(6,4)$.

Answer:

A reflection of the line segment across the y - axis