Question

a sequence of transformations is performed on △xyz, resulting in △xyz. both triangles are shown on the coordinate plane below.
some transformations are listed below.

• r₉₀: a rotation 90° counter - clockwise
• rₓ: a reflection across the x - axis
• rᵧ: a reflection across the y - axis

which of these describes the sequence of transformations performed on △xyz that results in △xyz?
a. rₓ followed by r₉₀
b. r₉₀ followed by rₓ
c. rᵧ followed by r₉₀

Explanation:

To determine the sequence of transformations, we can analyze the orientation and position of the original triangle $\triangle XYZ$ and the final triangle $\triangle X'Y'Z'$. A $90^{\circ}$ counter - clockwise rotation ($R_{90}$) changes the orientation of the figure. A reflection across the $x$ - axis ($R_x$) flips the figure over the $x$ - axis and a reflection across the $y$ - axis ($R_y$) flips it over the $y$ - axis. By observing the change in orientation and position of the vertices of the triangles, we can see that first a $90^{\circ}$ counter - clockwise rotation is done which changes the orientation of the triangle and then a reflection across the $x$ - axis flips it to the final position.

Answer:

B. $R_{90}$ followed by $R_x$