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

Step 1: Identify Original Coordinates

• From the graph, we can see the coordinates of the original vertices:
• \(W(-3, 4)\)
• \(X(-1, 4)\)
• \(Y(-2, 1)\)
• \(Z(-4, 3)\)

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

For a \(180^\circ\) rotation around the origin, the transformation is \((x, y)
ightarrow (-x, -y)\). We apply this to each vertex:

• For \(W(-3, 4)\):
• New \(x\)-coordinate: \(-(-3) = 3\)
• New \(y\)-coordinate: \(-4\)
• So, \(W'(3, -4)\)

• For \(X(-1, 4)\):
• New \(x\)-coordinate: \(-(-1) = 1\)
• New \(y\)-coordinate: \(-4\)
• So, \(X'(1, -4)\)

• For \(Y(-2, 1)\):
• New \(x\)-coordinate: \(-(-2) = 2\)
• New \(y\)-coordinate: \(-1\)
• So, \(Y'(2, -1)\)

• For \(Z(-4, 3)\):
• New \(x\)-coordinate: \(-(-4) = 4\)
• New \(y\)-coordinate: \(-3\)
• So, \(Z'(4, -3)\)

Answer:

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