Question

1. triangle fgh is transformed in the coordinate plane to form the image fgh. label the vertices of fgh and tell what single transformation was used.

Explanation:

Step1: Observe vertex - coordinates

Let's assume the coordinates of vertices of $\triangle FGH$ are $F(x_1,y_1)$, $G(x_2,y_2)$, $H(x_3,y_3)$. By looking at the graph, if $F(- 4,5)$, $G(-2,2)$, $H(-7,1)$. The coordinates of the vertices of $\triangle F'G'H'$ are $F'(4, - 5)$, $G'(2,-2)$, $H'(7,-1)$.

Step2: Analyze the transformation rule

We can see that for each vertex $(x,y)$ of $\triangle FGH$, the corresponding vertex $(x',y')$ of $\triangle F'G'H'$ follows the rule $(x,y)\to(-x,-y)$. This is the rule for a rotation of $180^{\circ}$ about the origin.

Answer:

The vertices of $\triangle F'G'H'$ are obtained by rotating the vertices of $\triangle FGH$ 180 - degrees about the origin. The transformation is a $180^{\circ}$ rotation about the origin.