Distance Between Sharon and Jacob After Their Walks

To find the distance between Jacob and Sharon, we can use the Pythagorean theorem.

1. Determine Jacob’s final position:

– He walked 3 m north and then 4 m west. So, from the starting point (0,0):

– North (y-axis): (0, 3)

– West (x-axis): (-4, 3)

– Jacob’s final position: (-4, 3)

2. Determine Sharon’s final position:

– She walked 5 m south and then 12 m east. So from the starting point (0,0):

– South (y-axis): (0, -5)

– East (x-axis): (12, -5)

– Sharon’s final position: (12, -5)

3. Calculate the distance between their positions using the formula:

[

d = sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}

]

Where ( (x_1, y_1) ) is Jacob’s position (-4, 3) and ( (x_2, y_2) ) is Sharon’s position (12, -5):

[

d = sqrt{(12 – (-4))^2 + (-5 – 3)^2}

]

[

=