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( , ) b. t( , ) of x - axis c. r(°, ( ) ) d. t( , ) of y - axis e. r (type an equation.)

Explanation:

Step1: Analyze the orientation change

By observing the two triangles $\triangle ABC$ and $\triangle DEF$, we can see that their orientation has changed. Rigid - motions include translations, rotations, and reflections. A translation just moves the figure without changing its orientation. Since the orientation has changed here, we consider rotation or reflection.

Step2: Check for reflection

If it was a reflection over the x - axis, the y - coordinates of the corresponding points would change signs. If it was a reflection over the y - axis, the x - coordinates of the corresponding points would change signs. By comparing the coordinates of the vertices of $\triangle ABC$ and $\triangle DEF$, we can see that it is not a simple reflection over the x - axis or y - axis.

Step3: Determine rotation

We can find the center of rotation (assume the origin $(0,0)$ for simplicity in a grid - based system like this). By observing the relative position of the triangles, we can see that $\triangle ABC$ is rotated $180^{\circ}$ counter - clockwise about the origin to get $\triangle DEF$. The rule for a $180^{\circ}$ counter - clockwise rotation about the origin for a point $(x,y)$ is $(x,y)\to(-x,-y)$.

Answer:

C. R$(180^{\circ},(0,0))$