Question

2 reflect △def across the y - axis. then rotate △def 90° counterclockwise around the origin. what are the coordinates of the vertices of △def? show your work.

Explanation:

Step1: Find coordinates after y - axis reflection

The rule for reflecting a point $(x,y)$ across the y - axis is $(-x,y)$. Assume the coordinates of $D=(x_1,y_1)$, $E=(x_2,y_2)$, $F=(x_3,y_3)$. From the graph, if $D = (-5,-2)$, $E=(0,-2)$, $F=(-3,-6)$. After reflection across the y - axis, $D'=(5,-2)$, $E'=(0,-2)$, $F'=(3,-6)$.

Step2: Find coordinates after 90 - degree counter - clockwise rotation

The rule for rotating a point $(x,y)$ 90 degrees counter - clockwise around the origin is $(-y,x)$.
For $D'=(5,-2)$, $D''=(2,5)$.
For $E'=(0,-2)$, $E''=(2,0)$.
For $F'=(3,-6)$, $F''=(6,3)$.

Answer:

The coordinates of $D''$ are $(2,5)$, the coordinates of $E''$ are $(2,0)$ and the coordinates of $F''$ are $(6,3)$.