Question

a line segment has endpoints at (-1, 4) and (4, 1). which reflection will produce an image with endpoints at (-4, 1) and (-1, -4)? a reflection of the line segment across the y = x a reflection of the line segment across the y = -x a reflection of the line segment across the x - axis a reflection of the line segment across the y - axis

Explanation:

Step1: Original endpoints

Original: $(-1, 4)$ and $(4, 1)$

Step2: Desired image endpoints

Desired: $(-4, 1)$ and $(-1, -4)$

Step3: Test reflection over $y=-x$

For $(-1, 4)$: $(-y, -x)=(-4, 1)$; For $(4, 1)$: $(-y, -x)=(-1, -4)$

Answer:

a reflection of the segment across the line $y=-x$