Question

The graph shows triangles FGH and F'G'H'.
Points: F (2, 1), G (8, 4) H (5, 5).
Points: F' (-3, -2), G' (-6, 4), H' (-7, 1).
Which sequences of transformations map FGH onto F'G'H'? Select all that apply.
A. A rotation 180 degrees around the origin followed by a translation right 1 unit and up 5 units.
B. A rotation 90 degrees counterclockwise around the origin followed by a translation left 2 units and down 4 units
C. A reflection across the y-axis followed by a rotation 90 degrees counterclockwise around the origin.
D. That translation left 4 units and up 2 units followed by a rotation 90 degrees counterclockwise around the origin.

Answer 1

B and D

Reason (quick check):
- For B: rotate 90° CCW: (x,y) -> (-y,x). Then translate left 2, down 4: (-y-2, x-4).
- F(2,1) -> (-1,2) -> (-3,-2) = F'
- G(8,4) -> (-4,8) -> (-6,4) = G'
- H(5,5) -> (-5,5) -> (-7,1) = H'

- For D: translate left 4, up 2: (x,y)->(x-4,y+2). Then rotate 90° CCW: (a,b)->(-b,a). Composite: (x,y)->(-(y+2), x-4) = (-y-2, x-4), same result as B, so it also maps FGH to F'G'H'.

A and C do not work (e.g., A sends F to (-1,4) not (-3,-2); C sends F to (-1,-2) not (-3,-2)).