Question

write the coordinates of the vertices after a rotation 180° counterclockwise around the origin.

Explanation:

1. First, identify the original coordinates of the vertices:

• Assume the vertices of the figure are \(V(x_1,y_1)\), \(U(x_2,y_2)\), \(W(x_3,y_3)\). From the graph, if we assume \(V(1, - 1)\), \(U(1, - 8)\), \(W(-9,-8)\).

1. Recall the rule for a \(180^{\circ}\) counter - clockwise rotation about the origin:

• The rule for a \(180^{\circ}\) counter - clockwise rotation about the origin \((0,0)\) for a point \((x,y)\) is \((x,y)\to(-x,-y)\).

1. Apply the rotation rule to each vertex:

• For vertex \(V(1, - 1)\):
• Using the rule \((x,y)\to(-x,-y)\), we substitute \(x = 1\) and \(y=-1\). So, \(V(1, - 1)\to V'(-1,1)\).
• For vertex \(U(1, - 8)\):
• Substitute \(x = 1\) and \(y=-8\) into the rule \((x,y)\to(-x,-y)\). Then \(U(1, - 8)\to U'(-1,8)\).
• For vertex \(W(-9,-8)\):
• Substitute \(x=-9\) and \(y = - 8\) into the rule \((x,y)\to(-x,-y)\). We get \(W(-9,-8)\to W'(9,8)\).

Step1: Identify original coordinates

Assume \(V(1, - 1)\), \(U(1, - 8)\), \(W(-9,-8)\)

Step2: Recall rotation rule

\((x,y)\to(-x,-y)\) for \(180^{\circ}\) counter - clockwise rotation about origin

Step3: Apply rule to \(V\)

Substitute \(x = 1,y=-1\) into \((-x,-y)\) to get \(V'(-1,1)\)

Step4: Apply rule to \(U\)

Substitute \(x = 1,y=-8\) into \((-x,-y)\) to get \(U'(-1,8)\)

Step5: Apply rule to \(W\)

Substitute \(x=-9,y=-8\) into \((-x,-y)\) to get \(W'(9,8)\)

Answer:

The new coordinates of the vertices are \(V'(-1,1)\), \(U'(-1,8)\), \(W'(9,8)\)