Problem sloving

Question

A car left point X and traveled 3 miles south, then 6 miles west, then 3 miles south, then another 3 miles east, and finally 6 miles south, arriving then at point Y. What is the straight line distance between X and Y?

Answer 1

Drawing a picture will help you a lot with this question! Use graph paper if you're unsure of the directions. (Remember west is left, east is right, north is up, and south is down when we're representing directions on paper.)

Since I can't post a picture, let's look at the directions we're given:

3 miles south, then 6 miles west, then 3 miles south, then another 3 miles east, and finally 6 miles south

1. In the vertical direction, the car travels 3+3+6 miles south, or 12 miles down on paper.
2. On the horizontal, the car travels 6 miles west and 3 miles east, for a total of 3 miles west, or 3 miles left on paper.

This can be drawn as a right triangle, with a vertical leg of length 12 and a horizontal leg of 3.

Using the Pythagorean theorem, a²+b²=c², plug 3 and 12 in for the legs and solve for c:

12²+3²=144+9=153, which is c².

We need c from c²=153.

Take the square root of both sides to get c=√153.

You can simplify √153 into √(9·17) = 3√17

or use a calculator to round it to 12.37 miles.

I hope this helps! Let me know if you have more questions.