Question

A highway map of Ohio has a coordinate grid superimposed on top of the state. Springfield is at point (1, –4) and Columbus is at point (7, 1). The Springfield youth soccer team is going to Columbus to see a professional soccer match. The map shows a highway rest area halfway between the cities. What are the coordinates of the rest area? What is the distance between Springfield and Columbus? (One unit = 5.38 miles)

Answer 1

The midpoint, where the rest area is, will just be the average of the coordinates of Springfield and Columbus.

Rest Area=((1+7)/2, (-4+1)/2)

Rest Area=(4, -1.5)

The distance between the two cities can be found using the Pythagorean Theorem, which used in the manner is often referred to as the "distance" formula between two points.

d^2=(x2-x1)^2+(y2-y1)

d^2=(7-1)^2+(1--4)^2

d^2=36+25

d^2=61

d=√61  and we are told that each unit is equal to 5.38mi so the distance from Springfield to Columbus is:

D=5.38√61 mi

D≈42.02mi  (to nearest hundredth of a mile)