Question

which sequence of transformations takes △a to its image, △b? a reflection over the x -axis and translation 2 units down b reflection over the y -axis and translation 2 units down c translation 2 units down and 90° rotation about the origin d translation 12 units right and 90° rotation about the origin

Explanation:

Step1: Analyze orientation change

The orientation of $\triangle A$ and $\triangle B$ is different. If we consider the vertices of the triangles, we can see that a rotation is involved. Also, there is a change in the position along the x - axis.

Step2: Check translation

The x - coordinate of the left - most vertex of $\triangle A$ is around - 8 and of $\triangle B$ is around 4. The difference in x - coordinates is $4-(-8)=12$, which means a translation of 12 units to the right.

Step3: Check rotation

After translation, we can observe that a $90^{\circ}$ rotation about the origin is required to match the orientation of $\triangle A$ to $\triangle B$.

Answer:

D. translation 12 units right and 90° rotation about the origin