Question

the vertices of $\triangle xyz$ are $x(2, 3)$, $y(-3, 2)$, and $z(-4, -3)$. translate $\triangle xyz$ using the given vector or rule. graph $\triangle xyz$ and its image.
$(x, y) \to (x + 3, y - 1)$

Explanation:

Step1: Translate point X

Given \( X(2, 3) \) and the rule \( (x, y) \to (x + 3, y - 1) \), substitute \( x = 2 \) and \( y = 3 \).
\( x + 3 = 2 + 3 = 5 \), \( y - 1 = 3 - 1 = 2 \). So the image of \( X \) is \( X'(5, 2) \).

Step2: Translate point Y

Given \( Y(-3, 2) \), substitute into the rule. \( x + 3 = -3 + 3 = 0 \), \( y - 1 = 2 - 1 = 1 \). So the image of \( Y \) is \( Y'(0, 1) \).

Step3: Translate point Z

Given \( Z(-4, -3) \), substitute into the rule. \( x + 3 = -4 + 3 = -1 \), \( y - 1 = -3 - 1 = -4 \). So the image of \( Z \) is \( Z'(-1, -4) \).

To graph: Plot \( X(2, 3) \), \( Y(-3, 2) \), \( Z(-4, -3) \) for \( \triangle XYZ \), and \( X'(5, 2) \), \( Y'(0, 1) \), \( Z'(-1, -4) \) for its image, then connect the vertices.

Answer:

The image vertices are \( X'(5, 2) \), \( Y'(0, 1) \), \( Z'(-1, -4) \). (Graphing involves plotting these points and connecting them as triangles.)