Question

Shape A can be transformed to shape B by a reflection in the x-axis followed by a translation (c, d) find the value of c and the value of d

Answer 1

c = -6

d = -1

Explanation:

In the picture attached, the question is shown.

Shape A is composed of the points:

(3, 2)

(5, 2)

(3, 5)

Reflection across the x-axis transforms point (x, y) into (x, -y). Applying this transformation to shape A:

(3, 2) → (3, -2)

(5, 2) → (5, -2)

(3, 5) → (3, -5)

Translation (c, d) transforms (x, y) into (x+c, y+d). The point (3, -2) in the pre-image (before translation) corresponds to point (-3,-3) in the image (after translation). Therefore:

(3, -2) → (3+c, -2+d) → (-3,-3)

3+c = -3

c = -3 -3 = -6

-2+d = -3

d = -3+2 = -1