Question

rotate this polygon 180°?
pre - image
coordinates\tnew x\tnew y
(0, - 8)\ti
(3, - 8)
(6, - 5)
(6,1)
(3,2)
(0,2)

Explanation:

Step1: Recall the rotation rule

When rotating a point \((x,y)\) \(180^{\circ}\) about the origin, the new coordinates are \((-x,-y)\).

Step2: Apply the rule to each point

• For \((0, - 8)\):

\(x = 0\), \(y=-8\). New \(x=-0 = 0\), new \(y=-(-8)=8\)

• For \((3,-8)\):

\(x = 3\), \(y = - 8\). New \(x=-3\), new \(y = 8\)

• For \((6,-5)\):

\(x = 6\), \(y=-5\). New \(x=-6\), new \(y = 5\)

• For \((6,1)\):

\(x = 6\), \(y = 1\). New \(x=-6\), new \(y=-1\)

• For \((3,2)\):

\(x = 3\), \(y = 2\). New \(x=-3\), new \(y=-2\)

• For \((0,2)\):

\(x = 0\), \(y = 2\). New \(x=-0=0\), new \(y=-2\)

Answer:

Pre - image Coordinates	New X	New Y
\((3,-8)\)	\(-3\)	\(8\)
\((6,-5)\)	\(-6\)	\(5\)
\((6,1)\)	\(-6\)	\(-1\)
\((3,2)\)	\(-3\)	\(-2\)
\((0,2)\)	\(0\)	\(-2\)