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lys-0071 [83]
3 years ago
10

Emma is playing miniature golf. Her ball is 2 feet to the left of the right-hand wall. The hole is 4 feet to the left of the wal

l. The distance along the wall between her ball and the hole is 18 feet. There is an obstacle between her ball and the hole, so Emma must hit her ball off the right-hand wall to reflect it towards the hole. How far down the wall should she aim?

Mathematics
1 answer:
NISA [10]3 years ago
8 0

Answer:

<u></u>

  • <u>She should aim 6 feet down the wall</u>

Explanation:

The diagram attached sketches the situtation.

Since the angle with which the ball hits the wall is the same with which it bounces, angle β is the same for the two shown triangles.

Then, since both are right triangles, then all the angles are congruent and the triangles are similar. Hence, you can equal the ratios of the sides, to make an equation:

  • x/4 = y/2 ⇒ x = 2y

You have other equation:

  • x+ y = 18

Substitute

  • 2y + y = 18
  • 3y = 18
  • y = 18/3
  • y = 6 ← this is the distance down the wall where the ball should hit

  • x = 2(6) = 12

Then, she should aim 6 feet down the wall.

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Let's start by calling the known endpoint L and the unknown K. We'll call the midpoint M. In order to find this, we must first note that to find a midpoint we need to take the average of the endpoints. To do this we add them together and then divide by 2. So, using that, we can write a formula and solve for each part of the k coordinates. We'll start with just x values.

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