Question

the rule $t_{5, -0.5} \circ r_{0, 180^\circ}(x, y)$ is applied to $\triangle fgh$ to produce $\triangle fgh$. what are the coordinates of vertex $f$ of $\triangle fgh$? the options are $(-0.5, 4)$, $(-1.5, 4)$, $(4, -1.5)$, $(4, -0.5)$ (accompanied by a graph of the triangle on a coordinate plane).

Explanation:

Step1: Determine original F coordinates

Assume F is (1, 0) from graph.

Step2: Apply 180° rotation

R₀,180°(1,0)=(-1, -0) = (-1, 0)

Step3: Apply translation T₅,-0.5

(-1+5, 0-0.5)=(4, -0.5)

Answer:

(4, -0.5)