Question

3 rotate the figure below 180° counterclockwise. click to select polygon abcd

Explanation:

Step1: Recall rotation rule

For a 180 - degree counter - clockwise rotation about the origin $(x,y)\to(-x,-y)$.

Step2: Identify vertices of original polygon

Let the vertices of polygon $ABCD$ be $A(x_1,y_1)$, $B(x_2,y_2)$, $C(x_3,y_3)$, $D(x_4,y_4)$. For example, if $A(- 3,3)$, $B(-2,2)$, $C(-3,1)$, $D(-4,2)$.

Step3: Apply rotation rule

$A(-3,3)\to A'(3,-3)$, $B(-2,2)\to B'(2,-2)$, $C(-3,1)\to C'(3,-1)$, $D(-4,2)\to D'(4,-2)$.

Step4: Plot new vertices

Plot $A'$, $B'$, $C'$, $D'$ and connect them to form polygon $A'B'C'D'$.

Answer:

The new polygon $A'B'C'D'$ is obtained by applying the rule $(x,y)\to(-x,-y)$ to each vertex of the original polygon $ABCD$ and then connecting the new vertices.