a line segment has endpoints at (-1, 4) and (4, 1). which reflection will produce an image with endpoints at…

Explanation:

Step1: Recall reflection rules

Reflection across x - axis: $(x,y)\to(x, - y)$; across y - axis: $(x,y)\to(-x,y)$; across $y = x$: $(x,y)\to(y,x)$; across $y=-x$: $(x,y)\to(-y,-x)$.

Step2: Check reflection across y - axis

For the point $(-1,4)$, reflection across y - axis gives $(1,4)$ (not correct).

Step3: Check reflection across x - axis

For the point $(-1,4)$, reflection across x - axis gives $(-1,-4)$; for the point $(4,1)$, reflection across x - axis gives $(4, - 1)$ (not correct).

Step4: Check reflection across $y = x$

For the point $(-1,4)$, reflection across $y = x$ gives $(4,-1)$ (not correct).

Step5: Check reflection across $y=-x$

For the point $(-1,4)$, reflection across $y=-x$ gives $(-4,1)$. For the point $(4,1)$, reflection across $y=-x$ gives $(-1,-4)$.

Answer:

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