Question

Triangle XYZ has coordinates X(2, 4), Y(−3, 4), and Z(−3, 1). If the triangle is translated using the rule (x, y) → (x − 2, y + 1), what are the coordinates of Y'?

Y'(–5, 5)
Y'(0, 5)
Y'(–5, 2)
Y'(–1, 3)

Answer 1

To find the new coordinates of point Y after the translation using the rule (x, y) → (x − 2, y + 1), we start with the coordinates of point Y, which are Y(−3, 4).

Now, we apply the translation:

1. For the x-coordinate:
\[
x' = x - 2 = -3 - 2 = -5
\]

2. For the y-coordinate:
\[
y' = y + 1 = 4 + 1 = 5
\]

So, the new coordinates after the translation are Y'(-5, 5).

Thus, the correct answer is \( Y'(-5, 5) \).