Question

graph the image of △fgh after a rotation 180° counterclockwise around the origin.

Explanation:

Step1: Recall rotation rule

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

Step2: Identify original points

Let's assume the coordinates of the vertices of $\triangle FGH$ are $F(x_1,y_1)$, $G(x_2,y_2)$ and $H(x_3,y_3)$. From the graph, if $F(8,3)$, $G(7,5)$ and $H(4,7)$.

Step3: Apply rotation rule

For point $F(8,3)$, after rotation, $F'( - 8,-3)$.
For point $G(7,5)$, after rotation, $G'( - 7,-5)$.
For point $H(4,7)$, after rotation, $H'( - 4,-7)$.

Step4: Graph new points

Plot the points $F'(-8,-3)$, $G'(-7,-5)$ and $H'(-4,-7)$ on the same coordinate grid and connect them to form the image of $\triangle FGH$ after a 180 - degree counter - clockwise rotation around the origin.

Answer:

Graph the points $F'(-8,-3)$, $G'(-7,-5)$ and $H'(-4,-7)$ and connect them to get the rotated triangle.