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2 years ago

7

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?

1 answer:

Ilya [14]2 years ago

7 0

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 $(x_1,y_1)$ and $(x_2,y_2)$ can be calculated using formula

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.$

Therefore, the distance between Jacob and Sharon is

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

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