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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
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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.

User Little Fox
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\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &H({{ 1}}\quad ,&{{ 10}})\quad % (c,d) &B({{ -3}}\quad ,&{{ -9}}) \end{array}\quad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ HB=√((-3-1)^2+(-9-10)^2)\implies HB=√((-4)^2+(-19)^2) \\\\\\ HB=√(377)\implies HB\approx 19.4\cdot \stackrel{meters}{100}\implies HB\approx 1940~m\\\\ -------------------------------\\\\


\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &Z({{ 10}}\quad ,&{{ 1}})\quad % (c,d) &B({{ -3}}\quad ,&{{ -9}}) \end{array}\quad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ ZB=√((-3-10)^2+(-9-1)^2)\implies HB=√((-13)^2+(-10)^2) \\\\\\ ZB=√(269)\implies ZB\approx 16.4\cdot \stackrel{meters}{100}\implies ZB\approx 1640~m
User Willy G
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7.7k points
6 votes
H(1,10) Z(10,1) B(-3,-9)
1st Calculate the distance H(horse) H to B(barn)
2nd Calculate the distance Z(horse) H to B(barn)
3rd Compare


1st distance H(horse) H to B(barn)
HB = √[(x₂-x₂)²+(y₂-y₁)₂] → √[-3-1)² + (-9-10)²]=√377 = 19.42

2nd distance ZB = √[(-3-10)²+(-9-1)²] = √269 = 16.4

HB in meter =19.42 x 100 = 1,942 m
ZB in meter = 16.4 x 100 = 1,640 m

Obviously HB > ZB and Z is closer to the Barn

User Larry Williamson
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8.2k points
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