Point A(2, 5) is dilated from the origin with scale factor 3, resulting in point A'. Darius says the coordinates of point A' are (6, 15). Marcia says the coordinates of point A' are (4, 13). Who is correct? O Darius Marcia

D=distance

VS=velocity through steel

VA=velocity through air

ts=time through steel

ta=time through air

Let's just get some equations out there:

D=VS*ts=16500*ts

D=VA*ta=1100*ta

ta=ts+6 (you can reason that it will take longer through air because the speed is slower)

So, D=16500*ts=1100*ta=D so 16500*ts=1100*ta. Substituting ts+6 in for ta we get 16500*ts=1100*(ts+6), so 16500*ts=1100*ts+6600. Subtracting 1100*ts from both sides, we get 15400*ts=6600, so ts=6600/15400=3/7 seconds. So, to find the distance, we need only plug this time back into the equation D=16500*ts=16500*3/7=7071.43 feet.