Question

find a congruence transformation that maps △vyw to △xnf. which congruence transformation maps the pre - image to the congruent image? select the correct choice below and fill in the answer boxes to complete you choice. a. t ◦ r(270°,0)(△vyw) b. t ◦ r(90°,0)(△vyw) c. t ◦ ry - axis(△vyw) d. t ◦ rx - axis(△vyw)

Explanation:

Step1: Analyze rotation rules

A $90^{\circ}$ counter - clockwise rotation about the origin $(x,y)\to(-y,x)$. A $270^{\circ}$ counter - clockwise rotation about the origin $(x,y)\to(y, - x)$. Reflection over the $x$ - axis $(x,y)\to(x,-y)$ and reflection over the $y$ - axis $(x,y)\to(-x,y)$.

Step2: Observe the triangles

By observing the positions of $\triangle VYW$ and $\triangle XNF$ on the coordinate grid, we can see that a reflection over the $y$ - axis maps $\triangle VYW$ to $\triangle XNF$. When we reflect a point $(x,y)$ of $\triangle VYW$ over the $y$ - axis to get $(-x,y)$ which corresponds to the points of $\triangle XNF$.

Answer:

C. $R_{y - axis}(\triangle VYW)$