Question

the figure to the right represents a miniature golf course hole. the ball is at p and the hole is at q.
a. explain how to aim the ball so that it gets in the hole, if it is to bounce off one wall only.
b. explain how to aim the ball so that it gets in the hole, if it is to bounce off two walls.

a. explain how to aim the ball so that it gets in the hole, if it is to bounce off one wall only. choose the correct answer below
a. reflect the midpoint of \\(\overline{pq}\\) in \\(\overline{ab}\\) to get \\(p\\). aim the ball at the intersection of \\(\overline{pp}\\) with \\(\overline{ab}\\)
b. aim the ball directly towards q.
c. drop a perpendicular from q to \\(\overline{ab}\\). aim the ball at the intersection of the perpendicular and \\(\overline{ab}\\)
d. reflect p in \\(\overline{ab}\\) to get \\(p\\). aim the ball at the intersection of \\(\overline{pq}\\) with \\(\overline{ab}\\)

Explanation:

When dealing with reflection - based aiming in such a geometric setup (miniature golf hole with walls), the principle of reflection is key. For bouncing off one wall (\(\overline{AB}\) in this case), we use the reflection property. If we reflect point \(P\) over the wall \(\overline{AB}\) to get \(P'\), then the line \(P'Q\) will intersect \(\overline{AB}\) at the point where the ball should hit the wall. This is based on the law of reflection (angle of incidence equals angle of reflection) which can be geometrically modeled using reflections.

• Option A: Reflecting the mid - point of \(\overline{PQ}\) is not the correct approach. The mid - point has no relation to the reflection - based aiming for a single - wall bounce.
• Option B: Aiming directly towards \(Q\) is not possible as there are walls in between (assuming the figure has non - transparent walls).
• Option C: Dropping a perpendicular from \(Q\) to \(\overline{AB}\) does not account for the position of \(P\) and the reflection principle.

Answer:

D. Reflect \(P\) in \(\overline{AB}\) to get \(P'\). Aim the ball at the intersection of \(\overline{P'Q}\) with \(\overline{AB}\)