Question

Please complete this completely !!! please help me yall

Answer 1

Answer:

(a)4 units, 3 units

(b) Right-angled triangle

Step-by-step 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

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Using the formula

$AB=\sqrt{(0-(-4))^2+(2-2)^2}=4units$

$BC=\sqrt{(0-0)^2+(5-2)^2}$

$BC=\sqrt{3^2}=3$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)

$CA=\sqrt{(-4-0)^2+(2-5)^2}$

$CA=\sqrt{16+9}=5$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.