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You walk 100 yards due south, then 120 yards due west, and then 30 yards due north. How far are you from your starting point?

Sagot :

Answer:

the distance = [tex]\bf 10\sqrt{193} \ yards\ (around\ 138.92\ yards)[/tex]

Step-by-step explanation:

We can find the distance from the starting point after walking 100 yards due south, 120 yards due west and 30 yards due north by using the Cartesian coordinate.

Let:

  • coordinate of starting point = (0, 0)
  • A = the point after walking 100 yards due south from starting point
  • B = the point after walking 120 yards due west from point A
  • C = the point after walking 30 yards due north from point B

Coordinate of point A:

[tex]\begin{aligned}(x_A,y_A)&=(x_0,(y_0-100))\\&=(0,(0-100))\\&=(0,-100)\end{aligned}[/tex]

Coordinate of point B:

[tex]\begin{aligned}(x_B,y_B)&=((x_A-120),y_A)\\&=((0-120),-100)\\&=(-120,-100)\end{aligned}[/tex]

Coordinate of point C:

[tex]\begin{aligned}(x_C,y_C)&=(x_B,(y_B+30))\\&=(-120,(-100+30))\\&=(-120,-70)\end{aligned}[/tex]

To find the distance between points (x₁, y₁) and (x₂, y₂), we use this formula:

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

Therefore the distance between the starting point and the final point (point C):

[tex]\begin{aligned}d&=\sqrt{(-120-0)^2+(-70-0)^2} \\&=\sqrt{19300} \\&=\bf 10\sqrt{193} \ yards\end{aligned}[/tex]

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