Question

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.

Answer 1

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

`d = \sqrt{(x_(2) - x_(1))^(2) + (y_(2) - y_(1))^(2)}`

The distance between horse H and the barn is

`d_(H) = \sqrt{(1+3)^(2) + (10+9)^2} =19.4165`
That is, 1941.64 m = 1.94 km (nearest hundredth).

The distance between horse Z and the barn is

`d_(Z) = \sqrt{(10+3)^(2) + (1+9)^(2)} =16.4012`
That is, 1640.12 m = 1.64 km (nearest hundredth)

Answer: Horse Z is closer to the barn.