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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 bu…

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 bu…
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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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2 Answers

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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
by
8.4k 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
by
8.4k points
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