(a)
Rotate triangle ABC 90° clockwise around the center of the graph and then reflect over the y-axis. Plot triangle DEF.
A 2, 3
B 2, 6
C 4, 3
To rotate triangle ABC 90° clockwise around the center of the graph, we can use the following formula for a 90° clockwise rotation:
x' = y
y' = -x
First, let's calculate the new coordinates for each point after the rotation:
Point A(2, 3) becomes A'(3, -2)
Point B(2, 6) becomes B'(6, -2)
Point C(4, 3) becomes C'(3, -4)
Now, to reflect the rotated triangle over the y-axis, we simply change the sign of the x-coordinate:
Point D'(3, 2)
Point E'(6, 2)
Point F'(3, 4)
So, triangle DEF after the transformation is as follows:
D(3, 2)
E(6, 2)
F(3, 4)