Question

the rule $t_{5, - 1.5}circ r_{y - axis}(x,y)$ is applied to $\triangle fgh$ to produce $\triangle fgh$. what are the coordinates of vertex $f$ of $\triangle fgh$? (4, - 1.5) (4, - 0.5) (- 1.5, 4) (- 0.5, 4)

Explanation:

Step1: Identify the transformation rules

The rule $T_{5, - 1.5}\circ R_{y - axis}$ means first reflect the point across the y - axis ($R_{y - axis}$) and then translate it 5 units to the right and 1.5 units down ($T_{5,-1.5}$).
Let's assume the original coordinates of point F are $(x,y)$. The rule for reflection across the y - axis is $(x,y)\to(-x,y)$. Then the rule for translation $T_{5,-1.5}$ is $(x,y)\to(x + 5,y-1.5)$. Combining these two transformations, if the original point is $(x,y)$, the final transformed point $(x',y')$ has coordinates $x'=-x + 5$ and $y'=y-1.5$.

Step2: Assume original coordinates of F

From the graph, assume the original coordinates of point F are $(1,0)$.
For reflection across the y - axis: $(1,0)\to(-1,0)$.
For translation: $x=-1+5 = 4$ and $y=0 - 1.5=-1.5$.

Answer:

$(4,-1.5)$