Yes, the distance from the merry-go-round to the water slide is the same as the distance from the water slide to the merry-go-round.
Given:
Coordinates of different rides in a park on the graph.
To find:
to find whether the distance from the merry-go-round to the water slide is the same as the distance from the water slide to the merry-go-round.
Solution:
The coordinates of merry-go-round = M = (8,2)
The coordinates of water slide = W = (8,-8)
The distance between the merry-go-round to the water slide.
Using distance formula, \((x_1,y_1);(x_2,y_2)\)::
\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
\(MW = \sqrt{(8-8)^2+(-8-2)^2}\\\\=\sqrt{(-10)^2}\\\\MW=10 units\)
The coordinates of water slide = W = (8,-8)
The coordinates of merry-go-round = M = (8,2)
The distance between the water slide to the merry-go-round:
Using distance formula, \((x_1,y_1);(x_2,y_2)\):
\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
\(WM = \sqrt{(8-8)^2+(2-(-8))^2}\\\\=\sqrt{(10)^2}\\\\MW=10 units\)
MW = WM = 10 units
Yes, the distance from the merry-go-round to the water slide is the same as the distance from the water slide to the merry-go-round.
Learn more about the distance formula here:
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