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.
