Question

graph the image of △def after a rotation 180° clockwise around the origin.

Explanation:

Step1: Recall rotation rule

The rule for a 180 - degree clockwise rotation around the origin is $(x,y)\to(-x,-y)$.

Step2: Identify original coordinates

Assume the coordinates of $\triangle DEF$ are $D(x_1,y_1)$, $E(x_2,y_2)$, $F(x_3,y_3)$. From the graph, if we assume $D(3, - 8)$, $E(7,-8)$, $F(3,-4)$.

Step3: Apply rotation rule

For point $D(3,-8)$, after rotation, $D'(-3,8)$.
For point $E(7,-8)$, after rotation, $E'(-7,8)$.
For point $F(3,-4)$, after rotation, $F'(-3,4)$.

Step4: Plot new points

Plot $D'(-3,8)$, $E'(-7,8)$ and $F'(-3,4)$ on the coordinate - plane and connect them to form the rotated triangle.

Answer:

Plot points $D'(-3,8)$, $E'(-7,8)$ and $F'(-3,4)$ and connect them to get the image of $\triangle DEF$ after a 180 - degree clockwise rotation around the origin.