Question

rotate △def 90° clockwise around the origin. then translate △def to the right 5 units and down 2 units. what are the coordinates of the vertices of △def? show your work.

Explanation:

Step1: Find original coordinates

Let's assume the coordinates of the vertices of $\triangle DEF$ are $D(x_1,y_1)$, $E(x_2,y_2)$, $F(x_3,y_3)$. From the graph, if we assume $D(- 1,5)$, $E(-1,1)$, $F(-5,1)$.

Step2: Apply 90 - degree clock - wise rotation formula

The formula for a 90 - degree clock - wise rotation about the origin is $(x,y)\to(y, - x)$.
For point $D(-1,5)$: After rotation, $D'(5,1)$.
For point $E(-1,1)$: After rotation, $E'(1,1)$.
For point $F(-5,1)$: After rotation, $F'(1,5)$.

Step3: Apply translation

The translation is 5 units to the right and 2 units down. The translation rule is $(x,y)\to(x + 5,y-2)$.
For $D'(5,1)$: $D''=(5 + 5,1-2)=(10,-1)$.
For $E'(1,1)$: $E''=(1 + 5,1-2)=(6,-1)$.
For $F'(1,5)$: $F''=(1 + 5,5-2)=(6,3)$.

Answer:

The coordinates of the vertices of $\triangle D'E'F'$ are $D''(10,-1)$, $E''(6,-1)$, $F''(6,3)$