Question

1. quadrilateral wxyz with vertices w(-6, 7), x(-3, 6), y(-1, 3), and z(-7, 1): 180°

Explanation:

To rotate a point \((x, y)\) 180° about the origin, we use the rule \((x, y) \to (-x, -y)\). We will apply this rule to each vertex of the quadrilateral.

Step 1: Find \(W'\)

The coordinates of \(W\) are \((-6, 7)\). Applying the 180° rotation rule:
\(x' = -(-6) = 6\)
\(y' = -7\)
So, \(W' = (6, -7)\)

Step 2: Find \(X'\)

The coordinates of \(X\) are \((-3, 6)\). Applying the 180° rotation rule:
\(x' = -(-3) = 3\)
\(y' = -6\)
So, \(X' = (3, -6)\)

Step 3: Find \(Y'\)

The coordinates of \(Y\) are \((-1, 3)\). Applying the 180° rotation rule:
\(x' = -(-1) = 1\)
\(y' = -3\)
So, \(Y' = (1, -3)\)

Step 4: Find \(Z'\)

The coordinates of \(Z\) are \((-7, 1)\). Applying the 180° rotation rule:
\(x' = -(-7) = 7\)
\(y' = -1\)
So, \(Z' = (7, -1)\)

Answer:

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