Two horses are ready to return to their barn after a long workout session at the track. The horses are at coordinates H(1,10) and z(10, 1). Their barns are located in the same building, which is at coordinates B(-3,-9). Each unit/grid on the coordinate plane represents 100 meters. Which horse is closer to the barn? Justify your answer.

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24-08-2017
Mathematics

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Two horses are ready to return to their barn after a long workout session at the track. The horses are at coordinates H(1,10) and z(10, 1). Their barns are located in the same building, which is at coordinates B(-3,-9). Each unit/grid on the coordinate plane represents 100 meters. Which horse is closer to the barn? Justify your answer.

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Аноним Аноним · Answer 1 · 2017-08-31T10:48:45+02:00

The given coordinates are
Barn, B (-3,-9),
Horse H: (1, 10),
Horse Z: (10, 1).

Each unit on the coordinate plane represents 100 m.

Note that the distance between two coordinates (x₁, y₁) and (x₂, y₂) is
[tex]d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}} [/tex]

The distance between horse H and the barn is
[tex]d_{H} = \sqrt{(1+3)^{2} + (10+9)^2} =19.4165[/tex]
That is, 1941.64 m = 1.94 km (nearest hundredth).

The distance between horse Z and the barn is
[tex]d_{Z} = \sqrt{(10+3)^{2} + (1+9)^{2}} =16.4012[/tex]
That is, 1640.12 m = 1.64 km (nearest hundredth)

Answer: Horse Z is closer to the barn.