Question

a line segment has endpoints at (3, 2) and (2, -3). which reflection will produce an image with endpoints at (3, -2) and (2, 3)? 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 $x - axis$ is $(x,y)\to(x, - y)$.

Step2: Apply rule to endpoints

For the point $(3,2)$, reflecting across the $x - axis$ gives $(3,-2)$. For the point $(2,-3)$, reflecting across the $x - axis$ gives $(2,3)$.

Answer:

a reflection of the line segment across the $x$-axis