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Charra [1.4K]
2 years ago
6

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:
ASHA 777 [7]2 years ago
5 0

Answer:

A reflection of the line segment across the line y = –x.

Step-by-step explanation:

Given : A line segment has endpoints at (–1, 4) and (4, 1).

To find : Which reflection will produce an image with endpoints at (–4, 1) and (–1, –4).

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

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

Reflection:   (–1, 4)  →→ (–4, 1)

                    (4, 1)→→→ (–1, –4).

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

(x ,y) →→ (–y, -x)

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

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

katrin2010 [14]2 years ago
4 0

Answer:- A reflection of the line segment across the line y = –x .


Explanation:-

A reflection over the line y = -x, the x-coordinate and y-coordinate interchange their places and they are negated (the signs are changed).

Given :- A line segment has endpoints at (–1, 4) and (4, 1) such that it reflects produce an image with endpoints at (–4, 1) and (–1, –4).

(-1, 4)→(-4, 1) and

(4, 1)→(-1, -4)

Thus this shows a reflection of the line segment across the line y = –x.

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