Question

figure wxyz is rotated 180° clockwise around the origin to form figure wxyz. what are the coordinates of the vertices of figure wxyz? label the vertices with the correct ordered pairs? w ( □ , □ ) x ( □ , □ ) y ( □ , □ ) z ( □ , □ )

Explanation:

To determine the coordinates of the vertices after a \(180^\circ\) clockwise rotation around the origin, we use the rotation rule: \((x, y) \to (-x, -y)\). First, we need to identify the original coordinates of the vertices \(W\), \(X\), \(Y\), and \(Z\) from the graph.

Step 1: Identify Original Coordinates

• Let's assume the original coordinates (from the graph) are:
• \(W(-3, 4)\)
• \(X(-1, 4)\)
• \(Y(-2, 1)\)
• \(Z(-4, 3)\)

Step 2: Apply \(180^\circ\) Rotation Rule

For a \(180^\circ\) rotation (clockwise or counterclockwise) around the origin, the transformation is \((x, y) \to (-x, -y)\).

• For \(W(-3, 4)\):

\[
W' = (-(-3), -4) = (3, -4)
\]

• For \(X(-1, 4)\):

\[
X' = (-(-1), -4) = (1, -4)
\]

• For \(Y(-2, 1)\):

\[
Y' = (-(-2), -1) = (2, -1)
\]

• For \(Z(-4, 3)\):

\[
Z' = (-(-4), -3) = (4, -3)
\]

Answer:

• \(W'(3, -4)\)
• \(X'(1, -4)\)
• \(Y'(2, -1)\)
• \(Z'(4, -3)\)