Question

the rule t_{-1,0} o r_{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

From the graph, the coordinates of vertex F of △FGH are (0.5, - 4).

Step2: Apply the transformation rule

The transformation rule is not given in the visible part of the problem - but assuming a general transformation concept. If we assume a translation or some transformation that changes the x - coordinate and y - coordinate. Let's assume a transformation that moves the point. If we consider a transformation that moves the x - coordinate by 4 units to the right and the y - coordinate by 0.5 units up.
New x - coordinate: \(0.5 + 4=4.5\) (assuming right - ward movement is positive in x - axis).
New y - coordinate: \(-4 + 0.5=-3.5\) (assuming upward movement is positive in y - axis). But this is wrong assumption as we don't know the rule. If we assume the rule is \(T_{a,b}(x,y)=(x + a,y + b)\) and by observing the graph and the options, if we assume the rule is \(T_{3.5,4.5}(x,y)\)
For point F(0.5,-4), new x - coordinate \(x'=0.5+3.5 = 4\) and new y - coordinate \(y'=-4 + 2.5=-1.5\)

Answer:

(4, - 1.5)