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

Question

6 days ago

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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 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

Mathematics

2 answers:

babunello [3.6K] · Answer 1 · 2026-02-26T20:50:10+03:00

Answer:

The line segment is reflected over the line y = –x.

Step-by-step explanation:

We have a line segment with endpoints at (–1, 4) and (4, 1).

To determine: What reflection will create an image with endpoints at (–4, 1) and (–1, –4).

Solution: Starting with endpoints at (–1, 4) and (4, 1).

After reflection, the new endpoints will be (–4, 1) and (–1, –4).

Reflection: (–1, 4) →→ (–4, 1)

(4, 1)→→→ (–1, –4).

It can be seen that the x-coordinate changes to –y and the y-coordinate changes to –x.

(x,y) →→ (–y, -x)

This showcases the rule of reflection across the line y = –x.

Therefore, it is a reflection of the line segment across the line y = –x.

zzz [4K] · Answer 2 · 2026-02-26T20:47:19+03:00

Answer: The image of the line segment as reflected across the line y = –x.

Explanation:

In reflecting across the line y = -x, the coordinates of x and y will switch positions, and their signs will also switch.

Given: The endpoints of a line segment are (–1, 4) and (4, 1), and their reflection results in the endpoints (–4, 1) and (–1, –4).

(-1, 4)→(-4, 1) and

(4, 1)→(-1, -4)

This demonstrates the reflection of the line segment across the line y = –x.