Question

Triangle XYZ is shown on the coordinate plane.

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 + 4, y − 1) and then reflected across the y-axis to create triangle X″Y″Z″, what is the location of X″?

(8, 4)
(−5, 2)
(−8, 4)
(−9, 2)

Answer 1

After translation and reflection, the location of X″ is (-8, 4).

Step-by-step explanation:

To find the location of X″ after the triangle XYZ is translated using the rule (x, y) → (x + 4, y − 1) and then reflected across the y-axis, we can apply the translation and reflection separately to the coordinates of X.

1. Translate the x-coordinate of X by adding 4: 4 + 4 = 8
2. Translate the y-coordinate of X by subtracting 1: 5 - 1 = 4
3. After the translation, X becomes (8, 4)
4. Reflect the x-coordinate of X across the y-axis: -8
5. After the reflection, X″ becomes (-8, 4)

Therefore, the location of X″ is (-8, 4).