Question

A new playground is in the shape of a square. On a scale drawing, the vertices of the playground’s coordinates are: (6,0.5)

, (6,−7.5)
, (−2,−7.5)
, (−2,0.5)
. How long is each side of the playground?

Answer 1

To find the length of each side of the square playground, we can calculate the distance between two consecutive vertices.

Using the distance formula, the distance between two points (x1, y1) and (x2, y2) is given by:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Let's calculate the length of each side:

Distance between (6, 0.5) and (6, -7.5):
Distance = sqrt((6 - 6)^2 + (-7.5 - 0.5)^2) = sqrt(0 + 49) = sqrt(49) = 7
Distance between (6, -7.5) and (-2, -7.5):
Distance = sqrt((-2 - 6)^2 + (-7.5 - (-7.5))^2) = sqrt((-8)^2 + 0^2) = sqrt(64 + 0) = sqrt(64) = 8
Distance between (-2, -7.5) and (-2, 0.5):
Distance = sqrt((-2 - (-2))^2 + (0.5 - (-7.5))^2) = sqrt(0 + 64) = sqrt(64) = 8
Distance between (-2, 0.5) and (6, 0.5):
Distance = sqrt((6 - (-2))^2 + (0.5 - 0.5)^2) = sqrt((6 + 2)^2 + 0^2) = sqrt(64 + 0) = sqrt(64) = 8
Therefore, each side of the square playground has a length of 8 units.