Question

1. triangle xyz with vertices x(3, -2), y(6, 1), and z(5, -7): 180° image of a grid with a triangle drawn on it x(, ) y(, ) z(, )

Explanation:

Step1: Recall 180° rotation rule

For a point \((x, y)\), a 180° rotation about the origin gives \((-x, -y)\).

Step2: Rotate \(X(3, -2)\)

Apply the rule: \(x = 3\), \(y = -2\). So \(X' = (-3, 2)\).

Step3: Rotate \(Y(6, 1)\)

Apply the rule: \(x = 6\), \(y = 1\). So \(Y' = (-6, -1)\).

Step4: Rotate \(Z(5, -7)\)

Apply the rule: \(x = 5\), \(y = -7\). So \(Z' = (-5, 7)\).

Answer:

\(X'(-3, 2)\), \(Y'(-6, -1)\), \(Z'(-5, 7)\)