Triangle XYZ is shown on the coordinate plane.
A triangle on the coordinate plane with vertices X at 0 comma 5, Y at 10 comma 3, and Z at 4 comma negative 1.
If triangle XYZ is translated using the rule (x, y) → (x − 3, y − 2) and then reflected across the y-axis to create triangle X″Y″Z″, what is the location of Z″?
(−7, 1)
(−3, −1)
(−1, −3)
(3, 3)
To find the location of Z″ after the translation and reflection, we first apply the translation rule to the coordinates of point Z:
Z: (4, -1) → (4 - 3, -1 - 2) → (1, -3)
After the translation, the coordinates of Z become (1, -3). To find the location of Z″ after reflecting across the y-axis, we change the sign of the x-coordinate:
Z'': (-1, -3)
Therefore, the location of Z″ is (-1, -3).
The correct answer is:
(−1, −3)