Question

trapezoid abcd is transformed according to the rule \\(r_{x-\text{axis}} \circ r_{o, 90^{\circ}}\\). what is the x-coordinate of a?
-3
-2
2
3

Explanation:

Identify the initial coordinates of point A

$$ A = (2, 3) $$

Apply the rotation transformation

$$ R_{O, 90^\circ}(x, y) = (-y, x) $$

$$ R_{O, 90^\circ}(2, 3) = (-3, 2) $$

Apply the reflection transformation

$$ r_{x\text{-axis}}(x, y) = (x, -y) $$

$$ A' = r_{x\text{-axis}}(-3, 2) = (-3, -2) $$

$$ x\text{-coordinate of } A' = -3 $$

Answer:

• (A) -3 (Correct answer)
• (B) -2
• (C) 2
• (D) 3