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 x - axis 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

Explanation:

Step1: Recall reflection rules

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

Step2: Apply 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