A coordinate grid is used to make a map of the park. The location of the drinking fountain is (-7, 3); the location of the bench is (2, 3); and the location of the center of the slide is (-7, -5). Plot these points (Hint: You can use the “draw” menu to draw on the coordinate plane)

(a) What is the distance from the center of the slide to the drinking fountain? Show your work.

(b) What is the distance from the drinking fountain to the bench? Explain your reasoning.

(c) What type of triangle is created by the three locations? Explain.

Part a: The distance from the center of the slide to the drinking fountain is 8 units.

Part b: The distance from the drinking fountain to the bench is 9 units.

Part c: The triangle created by the three locations is a right angled triangle.

Explanation:

Part a: The location of the drinking fountain is

The location of the center of the slide is

We need to find the distance from the center of the slide to the drinking fountain.

The distance can be determined using the formula,

Substituting the coordinates and , we get,

Thus, the distance from the center of the slide to the drinking fountain is 8 units.

Part b: The location of the drinking fountain is

The location of the bench is

The distance from the drinking fountain to the bench can be determined using the formula,

Substituting the coordinates and , we get,

Thus, the distance from the drinking fountain to the bench is 9 units.

Part c: Plotting the points , and in the graph and joining the points, we can see that the three locations make a right angled triangle.

Thus, the triangle created by the three locations is a right angled triangle.

The graph attached below shows the triangle created by the three locations.

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional