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 $(-x,y)$.

Step2: Apply rule to endpoints

Given endpoints $(- 4,-6)$ and $(-6,4)$. After reflecting across the $y$-axis, for the point $(-4,-6)$, the new point is $(4,-6)$; for the point $(-6,4)$, the new point is $(6,4)$.

Answer:

a reflection of the segment across the $y$-axis