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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.

Respuesta :

ivycoveredwalls
Distance between points [tex]\left(x_1,y_1\right)[/tex] and [tex]\left( x_2,y_2 \right)[/tex] is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]

Distance from H to B:

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

Distance from Z to B:

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

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