Question

write a rigid motion that produces the image △abc→△def. select the correct choice below, and fill in the answer box(es) within your choice. if your answer involves an angle, use an angle measure between 0° and 360°. a. t( , ) of x - axis b. t( , ) c. r (type an equation.) d. r(°, ()) e. t( , ) of y - axis

Explanation:

Step1: Analyze the transformation

By observing the graph, we can see that $\triangle ABC$ is translated to get $\triangle DEF$. The translation is a rigid - motion. To find the translation, we look at the change in the coordinates of corresponding vertices.
Let's take vertex $A$ and its corresponding vertex $D$. Suppose the coordinates of $A=(x_1,y_1)$ and $D=(x_2,y_2)$. By counting the grid - squares, we find that the $x$ - coordinate of each point in $\triangle ABC$ is increased by 4 and the $y$ - coordinate is increased by 0.
The translation rule for a point $(x,y)$ is $T_{(4,0)}(x,y)=(x + 4,y)$.

Step2: Check the options

Option A: $T_{(4,0)}$ represents a translation 4 units to the right (increase in $x$ - value by 4 and no change in $y$ - value), which is the correct rigid - motion for transforming $\triangle ABC$ to $\triangle DEF$.

Answer:

A. $T_{(4,0)}$