Question

jacob is playing miniature golf. he states that he cannot hit the ball from the start, bounce it off the back wall once, and reach the hole in one shot. is jacob correct?
trace and label a diagram to support your answer.
is jacob correct?
o a. jacob is incorrect. to make the shot, he should first reflect the starting position over the back wall. he should aim at the midpoint between the starting position and the reflection of the starting
position.
o b. jacob is correct. it is not possible to hit the ball from the start, bounce it off the back wall once, and reach the hole in one shot.
o c. jacob is incorrect. to make the shot, he should first reflect the hole over the back wall. then connect where he is starting with the reflection of the hole with a line. he should aim at the
intersection of the back wall with the line.
o d. jacob is incorrect. to make the shot, he should first reflect the hole over the back wall. he should aim at the midpoint between the hole and the reflection of the hole.

Explanation:

Step1: Understand the reflection principle

When reflecting a point over a line (in this case, the back - wall), the shortest path from a starting point \(S\) to a hole \(H\) via a reflection is based on the property that the angle of incidence equals the angle of reflection. The correct method is to reflect the hole (or the starting point) over the back - wall.

Step2: Analyze each option

• Option A: Reflecting the starting position over the back - wall and aiming at the mid - point between the starting position and its reflection is incorrect. The key is to relate the hole's position (after reflection) to the starting position.
• Option B: Jacob is incorrect. It is possible. By reflecting the hole over the back - wall and then connecting the starting position to the reflected hole, we can find the point on the back - wall to aim for.
• Option C: Reflecting the hole over the back - wall and then connecting the starting position to the reflection of the hole is the correct geometric method for finding the path of the ball (using the law of reflection, which is equivalent to the shortest - path principle in geometric optics).
• Option D: Reflecting the hole over the back - wall and aiming at the mid - point between the hole and its reflection is not the correct approach. The connection should be between the starting position and the reflected hole.

Answer:

C. Jacob is incorrect. To make the shot, he should first reflect the hole over the back wall. Then connect where he is starting with the reflection of the hole with a line. He should aim at the intersection of the back wall with the line.