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° counterclockwise - 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. rᵧ followed by r₉₀ b. r₉₀ followed by rᵧ c. rₓ followed by r₉₀

Explanation:

Step1: Analyze the orientation change

First, observe that the triangle's orientation has changed in a way that a rotation is involved. If we consider the initial and final positions of the triangle, a \(90^{\circ}\) counter - clockwise rotation (\(R_{90}\)) will change the orientation of the triangle. After a \(90^{\circ}\) counter - clockwise rotation, the triangle is in a position where a reflection across the \(y\) - axis (\(R_y\)) will map it to the final position.

Step2: Check option B

Let's assume a point \((x,y)\) on \(\triangle XYZ\). A \(90^{\circ}\) counter - clockwise rotation \(R_{90}\) transforms \((x,y)\) to \((-y,x)\). Then a reflection across the \(y\) - axis \(R_y\) transforms \((-y,x)\) to \((y,x)\) which is consistent with the transformation from \(\triangle XYZ\) to \(\triangle X'Y'Z'\).

Answer:

B. \(R_{90}\) followed by \(R_y\)