Question

which congruence transformation maps stu to pqr?
a. rotation 90 degrees clockwise
b. rotation 90 degrees counterclockwise
c. rotation 180 degrees
d. reflection across the y - axis

Explanation:

To determine the congruence transformation, we analyze each option.

• Option A: A \(90^{\circ}\) clockwise rotation. If we consider a general point \((x,y)\) in \(STU\) and apply a \(90^{\circ}\) clockwise rotation formula \((x,y)\to(y, - x)\), we can check the positions of vertices. For example, assume a vertex of \(STU\) has coordinates \((- 4,-5)\) (approximate from the grid). After \(90^{\circ}\) clockwise rotation \((-4,-5)\to(- 5,4)\) (not matching \(PQR\) vertices).
• Option B: A \(90^{\circ}\) counter - clockwise rotation. Using the formula \((x,y)\to(-y,x)\). For a vertex like \((-4,-5)\) (approximate from \(STU\)), we get \((5,-4)\) (not matching \(PQR\) vertices).
• Option C: A \(180^{\circ}\) rotation. The formula for a \(180^{\circ}\) rotation is \((x,y)\to(-x,-y)\). If we take a vertex of \(STU\) say \((-4,-5)\), after \(180^{\circ}\) rotation we get \((4,5)\) (not matching \(PQR\) vertices).
• Option D: Reflection across the \(y\) - axis. The formula for reflection across the \(y\) - axis is \((x,y)\to(-x,y)\). If we consider the vertices of \(STU\) (e.g., if a vertex has coordinates \((-a,b)\) in \(STU\)), after reflection across the \(y\) - axis, it will have coordinates \((a,b)\) which matches the vertices of \(PQR\) as per the grid (by observing the symmetry about the \(y\) - axis).

Answer:

D. reflection across the y - axis