Find the coordinates of the vertices of the triangle after a reflection across the line x= -1 and then across the line y = 1. F(-2,-3), G(-3,2), H(1,-1)

  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

How we found the transformation

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)