Middle school math finding the distance

Question

You and your friend are standing back to back. Your friend runs 13 feet forward and 3 feet right. At the same time, you run 11 feet forward and 7 feet right. You stop and throw a baseball to your friend. How far fid you throw it.

Please provide an explanation.

Answer 1

graph the positions with starting points at the origin, (0,0)

Your friend runs 13 forward and 3 to the right. That's the point (13,-3)

You run 11 feet foward and 7 right, that's the point (-11, 7)

use the distance formula to calculate the distance between those two points

construct a right triangle with sides = 24 and 10. use the Pythagorean Theorm

square of the hypotenuse = sum of squares of the two sides

d^ = 24^2 + 10^2

d = square root of ( (13--11)^2 + (-3-7)^2 )

d = sqr(24^2 +10^2)

d = sqr676

d = 26 feet