Question

While playing mini golf, you hit the ball off of a wall to attempt at making it in the hole. The ball is located at (5,4) and the hole is located at (9,8). The point where the ball hits the wall is (7,0). Write an equation for the path of the ball and then determine if you will make your putt.

Answer 1

@Shadow

Answer 2

@Vocaloid

Answer 3

@Hero

Answer 4

So using the balls location and where it hits the wall, you can calculate the slope using:
\[m = \frac{ y_{2} - y_{1} }{ x_{2} - x_{1} }\]
then using point slope form you can write an equation for the line it makes
Point-Slope Form
\[y - y_{1} = m(x - x_{1})\]

Answer 5

I don't know if we're supposed to assume it follows the same slope after it bounces off the wall, but you're going to have to graph these points out then see if the ball after it bounces off the wall, can reach (9,8) with the slope you determined.

Answer 6

well i got the slope as 1

Answer 7

\[\frac{ 0 - 4 }{ 7 - 5 } = \frac{ -4 }{ 2 } = -2\]

Answer 8

oh okay my calculatinos were incooreect :(

Answer 9

okay and then i do

Answer 10

0-4=-2(7-5)

Answer 11

You could graph it out and see if from (7,0) at slope 2, it can reach (9,8).

Answer 12

Since it's bouncing off the wall, it's velocity (direction) would change to positive.

Answer 13

4

Answer 14

if you solve

Answer 15

it is reaching 9,8

Answer 16

Let's math this out:
y - 0 = -2(x - 7)
y = -2x + 14

This is the equation for the ball -> wall

From wall -> hole we can say it needs to using the slope of positive two since it's going up now.

y - 8 = 2(x - 9)
y - 8 = 2x - 18
y = 2x + 10

The two lines have different y intercepts but the same slopes (with signs changed), so it's not going to make it.

Answer 17

Wait hold on I got it.

Using the wall, we just write an equation for it with a positive slope, because then it'll be going in the other direction.

y - 0 = 2(x - 7)
y = 2x - 14

Answer 18

I graphed it out on Desmos so you can visualize it here: https://www.desmos.com/calculator/dyqpkdtynf

Answer 19

See how with the 2nd equation it misses (9, 8) completely

Answer 20

ohhhh

Answer 21

yes i see it

Answer 22

it doesnt pass through

Answer 23

Yes

Answer 24

thank you do muvh

Answer 25

Yeah I had to turn on some brain cells for it but np