Question

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

Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated \(180^{\circ}\) counter - clockwise around the origin, the new coordinates are \((-x,-y)\).

Step2: Find coordinates of \(E\)

The coordinates of \(E\) are \((-6,1)\). After rotation, \(x=-6,y = 1\), new \(x=6\), new \(y=-1\). So \(E'\) is \((6,-1)\).

Step3: Find coordinates of \(F\)

The coordinates of \(F\) are \((-6,10)\). After rotation, \(x=-6,y = 10\), new \(x=6\), new \(y=-10\). So \(F'\) is \((6,-10)\).

Step4: Find coordinates of \(G\)

The coordinates of \(G\) are \((0,10)\). After rotation, \(x = 0,y=10\), new \(x=0\), new \(y=-10\). So \(G'\) is \((0,-10)\).

Step5: Find coordinates of \(H\)

The coordinates of \(H\) are \((0,2)\). After rotation, \(x = 0,y=2\), new \(x=0\), new \(y=-2\). So \(H'\) is \((0,-2)\).

Answer:

\(E'(6,-1)\), \(F'(6,-10)\), \(G'(0,-10)\), \(H'(0,-2)\)