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Sharon and Jacob started at the same place. Jacob walked 3 m north and then 4 m west. Sharon walked 5 m south and 12 m east. How far apart are Jacob and Sharon now?

Respuesta :

frika

Consider the coordinate plane:

1. The origin is the point where Sharon and Jacob started - (0,0).

2. North - positive y-direction, south - negetive y-direction.

3. East - positive x-direction, west - negative x-direction.

Then,

  • if Jacob walked 3 m north and then 4 m west, the point where he is now has coordinates (-4,3);
  • if Sharon walked 5 m south and 12 m east, the point where she is now has coordinates (12,-5).

The distance between two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] can be calculated using formula

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

Therefore, the distance between  Jacob and Sharon is

[tex]D=\sqrt{(12-(-4))^2+(-5-3)^2}=\sqrt{16^2+8^2}=\sqrt{256+64}=\sqrt{320}=8\sqrt{5}\approx 11.18\ m.[/tex]

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