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 are Jacob and Sharon now?
A 5 m
B 8 m
C 13 m
D 18 m
E 24 m
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 are Jacob and Sharon now?
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To find out how far Jacob and Sharon are from each other, we can determine their positions on a coordinate plane.
1. Jacob’s journey:
– Starts at the origin (0, 0).
– Walks 3 m north: (0, 3).
– Walks 4 m west: (-4, 3).
2. Sharon’s journey:
– Starts at the origin (0, 0).
– Walks 5 m south: (0, -5).
– Walks 12 m east: (12, -5).
Now, we need to find the distance between Jacob’s position (-4, 3) and Sharon’s position (12, -5).
We can use the distance formula:
[
text{Distance} = sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}
]
where ((x_1, y_1)) is Jacob’s position and ((x_2, y_2)) is Sharon’s position.
Substituting the coordinates:
[
text{Distance} = sqrt{(12 – (-4))^2 + (-5 – 3)^2} = sqrt{(12 + 4)^2 + (-8)^2} = sqrt{16^2 + (-8)^2}
]
[
= sqrt{256