Triangle XYZ is shown on the coordinate plane.

Question

Triangle XYZ on the coordinate plane with ordered pairs at X 4, 5, at Y 5, 3, at Z 1, 3

If triangle XYZ is translated using the rule (x, y) → (x + 1, y − 4) and then reflected across the x-axis to create triangle X″Y″Z″, what is the location of Y″?

(−1, 6)
(2, 1)
(5, −1)
(6, 1)

Answer 1

To find the location of Y″ after the translation and reflection, we first apply the translation rule to the original coordinates of Y (5, 3).

After translating, the new coordinates of Y are:
x = 5 + 1 = 6
y = 3 - 4 = -1

Now, we reflect the translated point Y′(6, -1) across the x-axis.

The x-coordinate remains the same, and the y-coordinate becomes the opposite of the original y-coordinate:
Y″ = (6, -1)

Therefore, the correct answer is (6, -1).