Find the value of y when x equals 4, -3x+9y=-57

The distance between drinking fountain and bench is 4 units

The distance between bench and center of slide is 3 units

The right angled triangle is formed by the three locations.

Step-by-step explanation:

The location of the drinking fountain is (-4, 2)

The location of the bench is (0, 2)

The location of the center of the slide is (0, 5)

Part a) What is the distance from the drinking fountain to the bench? What is the distance from the bench to the center of the slide?

To find  the distance from the drinking fountain to the bench we will use distance formula:

The location of the drinking fountain is

The location of the bench is

Substitute the values in the formula

Thus the distance between drinking fountain and bench is 4 units

Now to find  the distance from the bench to the center of the slide

The location of the bench is

The location of the center of the slide is

Substitute the values in the formula

Thus the distance between bench and center of slide is 3 units

Now calculate the distance between drinking fountain and center of slide

The location of the drinking fountain is

The location of the center of the slide is

Thus the distance between drinking fountain and center of slide is 5 units

Part b) What type of triangle is created by the three locations?

The sides of the triangle formed by these points are of length 3 units , 4 units , 5 units

Check whether it satisfies Pythagoras theorem

So,the right angled triangle is formed by these points since it satisfies the Pythagoras theorem.

Hence the right angled triangle is formed by the three locations.