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)

Explanation:

Step1: Identify coordinates of Y

The coordinates of point \( Y \) are \( (-3, 4) \).

Step2: Apply translation rule

The translation rule is \( (x, y) \to (x - 2, y + 1) \). For point \( Y(-3, 4) \), substitute \( x = -3 \) and \( y = 4 \) into the rule.

• For the \( x \)-coordinate: \( x' = -3 - 2 = -5 \)
• For the \( y \)-coordinate: \( y' = 4 + 1 = 5 \)

Answer:

\( Y'(-5, 5) \)