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. a reflection of the line segment across the x-axis
• B. a reflection of the line segment across the y-axis
• C. a reflection of the line segment across the line $y=x$
• D. a reflection of the line segment across the line $y=–x$

Answer 1

The correct option is D

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

Explanation for the correct option:

We have given that endpoints at $(–1,4)$and $(4,1)$.

After reflection endpoints become $(–4,1)$ and $(–1,–4)$.

Reflection: $(–1,4)\to \to (–4,1)$

$(4,1)\to \to (–1,–4)$.

We can see $x$ coordinate become $-y$ coordinate and $y$ coordinate become $-x$ coordinate.

$(x,y)\to \to (–y,-x)$

This is the a reflection of the line segment across the line $y=–x$ rule of reflection .

Therefore, option $\left(D\right)$ is the correct answer.