Question

Please complete this completely !!! please help me yall

A coordinate grid is used to make a map of the park. The location of the drinking fountain is
(-4, 2); the location of the bench is (0, 2) ; and the location of the center of the slide is (0, 5).
(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? Explain your reasoning.
(b) What type of triangle is created by the three locations? Explain.
Answer:

Answer 1

(A) The distance from the drinking fountain to the bench is 4, and the distance from the bench to the center of the slide is 3 because if you add -4 and 0 you will get 4 and if you subtract 5 and 2 you will get 3.

(B) The type of triangle that is created is an right angle triangle because when you connect the 3 locations it creates an right angle triangle on the coordinate

Explanation:

Answer 2

(a)4 units, 3 units

(b) Right-angled triangle

Explanation:

We are given that

Let location of drinking fountain, A =(-4,2)

Location of the bench, B=(0,2)

Location of the center of the slide ,C=(0,5)

a. Distance formula

`√((x_2-x_1)^2+(y_2-y_1)^2)`

Using the formula

`AB=√((0-(-4))^2+(2-2)^2)=4units`

`BC=√((0-0)^2+(5-2)^2)`

`BC=√(3^2)=3`units

Hence, the distance from the drinking fountain to the bench=4 units

The distance from the bench to the center of the slide=3 units

(b)

`CA=√((-4-0)^2+(2-5)^2)`

`CA=√(16+9)=5`units

`AB^2+BC^2=4^2+3^2=16+9`

`AB^2+BC^2=25`

`CA^2=5^2=25`

`AC^2=AB^2+BC^2`

The triangle ABC satisfied the Pythagoras theorem. Hence, the triangle ABC is a right angled triangle.