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
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using the formula
[tex]AB=\sqrt{(0-(-4))^2+(2-2)^2}=4units[/tex]
[tex]BC=\sqrt{(0-0)^2+(5-2)^2}[/tex]
[tex]BC=\sqrt{3^2}=3[/tex]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)
[tex]CA=\sqrt{(-4-0)^2+(2-5)^2}[/tex]
[tex]CA=\sqrt{16+9}=5[/tex]units
[tex]AB^2+BC^2=4^2+3^2=16+9[/tex]
[tex]AB^2+BC^2=25[/tex]
[tex]CA^2=5^2=25[/tex]
[tex]AC^2=AB^2+BC^2[/tex]
The triangle ABC satisfied the Pythagoras theorem. Hence, the triangle ABC is a right angled triangle.
