Question

Which point would map onto itself after a reflection across the line y = –x? (–4, –4) (–4, 0) (0, –4) (4, –4)

Answer 1

The answer
first, put all point on the figure, and then trace graphe of y = -x
after, that we should find the image of each point, after a reflection across the line y = -x.
and we should find that the point would map onto itself after a reflection is        (–4, –4)

for more explanation, please look at the image. 

Answer 2

Answer:

The required point is (4, -4)

Step-by-step explanation:

For any point to map onto itself after reflection across the line, The first condition is that the point must lie on the line.

So, check the given points which lie on the equation of the given line :

y = -x

• (-4, -4)

y = -4 and -x = - (-4) = 4

⇒ y ≠ -x

So, (-4, -4) is rejected.

• (-4, 0)

y = -4 and -x = 0

⇒ y ≠ -x

So, (-4, 0) is rejected.

• (0, -4)

y = 0 and -x = - (-4) = 4

⇒ y ≠ -x

So, (0, -4) is rejected.

• (4, -4)

y = 4 and -x = - (-4) = 4

⇒ y = -x

So, (4, -4) is the required point which would map onto itself after a reflection across the given line y = -x

Hence, the required point is (4, -4)