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?

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