Question

Distance To find the distance between the swing and the sandbox in his backyard, Darren made a graph and found the coordinates of the swing to be (7, 2) and the coordinates of the sandbox to be (-3,8). Find the distance between the swing and the sandbox to the nearest tenth of a unit. ​

Answer 1

The distance between the swing and the sandbox is 11.7 units

Explanation:

The distance between points (x1, y1) and (x2, y2) is

d =
`\sqrt{(x2-x1)^(2)+(y2-y1)^(2)}`

Let us use this rule to solve the question

∵ Darren located the swing at point (7, 2)

∵ She located the sandbox at point (-3, 8)

∴ x1 = 7 and y1 = 2

∴ x2 = -3 and y2 = 8

→ Substitute them in the rule above

∴ d =
`\sqrt{(-3-7)^(2)+(8-2)^(2)}=\sqrt{(-10)^(2)+(6)^(2)}`

∴ d =
`√(100+36)=√(136)`

→ Find the value of the root

∴ d = 11.66190379

→ Round it to the nearest tenth

∴ d = 11.7 units

∴ The distance between the swing and the sandbox is 11.7 units