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 point Y'' after the transformations, we will follow the steps of translation and reflection one by one.

1. Translation: The translation rule given is (x, y) → (x + 1, y - 4). We start with the coordinates of point Y, which is at (5, 3).

   Applying the translation: \[ Y' = (5 + 1, 3 - 4) = (6, -1) \]

2. Reflection across the x-axis: When we reflect a point (x, y) across the x-axis, the new coordinates become (x, -y). We will reflect the point Y', which is at (6, -1).

   Applying the reflection: \[ Y'' = (6, -(-1)) = (6, 1) \]

Thus, the location of point Y'' is \((6, 1)\).

The final answer is: (6, 1)