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

Distance between points $\left(x_1,y_1\right)$ and $\left( x_2,y_2 \right)$ is

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2$

Distance from H to B:

$[tex]d=\sqrt{(10-(-3))^2+(1-(-9))^2}=\sqrt{169+100}=\sqrt{269}$d=\sqrt{(1-(-3))^2+(10-(-9))^2}=\sqrt{16+361}=\sqrt{376}[/tex] units.

Distance from Z to B:

$d=\sqrt{(10-(-3))^2+(1-(-9))^2}=\sqrt{169+100}=\sqrt{269}$ units.

Horse Z is closer to the barn.

(The conversion to meters is not required; the question does not ask for actual distances, so "units" is OK.)