Answer:
c). a reflection across the x-axis followed by a translation of 1 unit right and 1 unit down
Explanation:
You want to know the transformations that map ΔABC onto ΔDEF.
Transformations
The answer choices would ask us to consider some combination of the following transformations:
- reflection across the y-axis: (x, y) ⇒ (-x, y)
- reflection across the x-axis: (x, y) ⇒ (x, -y)
- reflection across the line y=x: (x, y) ⇒ (y, x)
- clockwise rotation 90°: (x, y) ⇒ (y, -x)
- positive rotation 270°: (x, y) ⇒ (y, -x) . . . same as 90° CW
- translation by (h, k): (x, y) ⇒ (x+h, y+k) . . . h units right, k units up
Application
We can apply these relations to the answer choices to see if they provide the desired mapping ...
- A(-4, 1) ⇒ D(-3, -2)
- B(-6, 5) ⇒ E(-5, -6)
- C(-1, 2) ⇒ F(0, -3)
a) Reflection across the y-axis, translation (1, 2)
A(-4, 1) ⇒ A'(4, 1) . . . reflection
A'(4, 1) ⇒ D(4+1, 1+2) = D(5, 3) . . . . not the correct point
b) Rotation CW 90°, translation (4, 4)
A(-4, 1) ⇒ A'(1, 4) . . . rotation 90° CW
A'(1, 4) ⇒ D(1+4, 4+4) = D(5, 8) . . . . not the correct point
c) Reflection across the x-axis, translation (1, -1)
A(-4, 1) ⇒ A'(-4, -1) . . . reflection
A'(-4, -1) ⇒ D(-4+1, -1+(-1)) = D(-3, -2) . . . . the correct location of D
d) Reflection across y=x, rotation CCW 270°
A(-4, 1) ⇒ A'(1, -4) . . . reflection
A'(1, -4) ⇒ D(-4, -1) . . . . not the correct point
The correct series of transformations is reflection across the x-axis followed by translation 1 right and 1 down.