Answer:
a. F'(0, 5), G'(1, 0), H'(-3, 3)
Step-by-step explanation:
Reflection across x = -1 gives you the transformation ...
(x, y) ⇒ (-2 -x, y)
Reflection across y = 1 gives you the transformation ...
(x, y) ⇒ (x, 2 -y)
Together, these give you the transformation ...
(x, y) ⇒ (-2 -x, 2 -y)
Applying this to point F, we have ...
F(-2, -3) ⇒ F'(-2 -(-2), 2 -(-3)) = F'(0, 5) . . . . . . matches choice A
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<em>How we found the transformation</em>
In general, if M is the midpoint between A and B, then you have ...
M = (A+B)/2
2M = A+B
B = 2M - A
So, if we want x=-1 to be the midpoint between x' and x, then we have ...
x' = 2(-1) -x = -2 -x
Likewise, if we want y=1 to be the midpoint between y' and y, then we have ...
y' = 2(1) -y = 2 -y
So, the transformation is ...
(x, y) ⇒ (x', y') = (-2 -x, 2 -y)
