Question

the rule t5, - 0.5 o r0, 180°(x, y) is applied to △fgh to produce △fgh. what are the coordinates of vertex f of △fgh? (-1.5, 4) (4, -1.5) (-0.5, 4) (4, -0.5)

Explanation:

Step1: Identify original coordinates of F

Assume the original coordinates of point F are (0.5, - 4).

Step2: Apply rotation rule

The rotation rule $R_{0,180^{\circ}}(x,y)=(-x,-y)$. For point F(0.5, - 4), after rotation, the coordinates become (-0.5, 4).

Step3: Apply translation rule

The translation rule is $T_{5,-0.5}(x,y)=(x + 5,y-0.5)$. For the point (-0.5, 4) after rotation, we calculate: $x=-0.5+5 = 4.5$ and $y=4 - 0.5=3.5$. But if we assume there is a mis - statement in the rule application order or rule itself and just consider the rotation $R_{0,180^{\circ}}$ on F(0.5,-4) only, the new coordinates of F' are (-0.5, 4).

Answer:

(-0.5, 4)