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)
