A' = (3, -1)
B' = (0 -3)
C' = (2, -4)
Explanation:
Given:
A = (1, -3)
B = (3, 0)
C = (4, -2)
First we will apply the 90 degrees counterclockwise rotation:
interchange x and y, then negate the new x value
[tex]\begin{gathered} (x,\text{ y) }\rightarrow\text{ (-y, x)} \\ A\text{ becomes: (-(-3), 1) = (3, 1)} \\ B\text{ becomes: (-0, 3) = (0, 3)} \\ C\text{ becomes: (-(-2), }4\text{) = (2, 4)} \end{gathered}[/tex]
Next we will apply reflection over the x axis:
negate y coordinate while keeping x coordinate constant
[tex]\begin{gathered} (x,\text{ y) }\rightarrow(x,\text{ -y)} \\ (3,\text{ 1) becomes (3 -1)} \\ A^{\prime}\text{ = (3, -1)} \\ \\ (0,\text{ 3) becomes (0, -3)} \\ B^{\prime}\text{ = (0, -3)} \\ \\ (2,\text{ 4) becomes (2, -4)} \\ C^{\prime}\text{ = (2, -4)} \end{gathered}[/tex]
