Question

A family is planning a vacation in which to travel from their home in Oregon to the home of relatives who live in North Carolina. The coordinates as their home on a map were (116,27), and the coordinates of the relative's home on the map are (33, 51). If each map coordinate represents 55 kilometers, what is the distance between the two homes to the nearest mile?​

Answer 1

The distance between the two homes is approximately 68 miles.

Step-by-step explanation:

To find the distance between the two homes, we can use the distance formula from coordinate geometry.

The formula to find the distance between two points (x1, y1) and (x2, y2) is:

distance = √((x2 - x1)^2 + (y2 - y1)^2)

Using the given coordinates, we have:

distance = √((33 - 116)^2 + (51 - 27)^2) km

distance = √((-83)^2 + (24)^2) km

distance = √(6889 + 576) km

distance = √7465 km

Converting km to miles, we have:

distance ≈ √7465 × 0.62 miles

distance ≈ √4631.3 miles

Since we're looking for the distance to the nearest mile, the distance between the two homes is approximately 68 miles.