Question

Tony took a city bus from his dorm to the school library, and then to a gym for a workout

before returning to his dorm. The coordinates (12, 6), (12, 15), (4, 0) represent the
locations of his stops respectfully on a city map. If each unit on the coordinate plane
represents 0.75 miles, how far did Tony ride on the city bus?

Answer 1

27 miles.

Explanation:

Here I attach the draw of the coordinates.

Tony traveled 3 segments. The first was from (12,6) to (12, 15), where, leting 12 constant, he moved from 6 to 15 in the ordinates axis, which implies 9 units. This is the section 1 in the draw.

Then he moved from point B to C. If you notice, this distance is the hypotenuse on the the triangle DBC. We can find this value using Pitagoras' theorem:

DB^2 + CD^2 = CB^2

With DB=15 and CD=8 (12 minus 4 = 8)

15^2 + 8^2 = 289

So CB^2=289

Applying sqr root:

CB = 17

So, the second section has a measure of 17 units.

Finally, the 3rd section is the hypotenuse of the DAC triangle and we can use Pitagoras to solve it:

CD^2 + AD^2 = CA^2

8^2 + 6^2 = CA^2

64 + 36 = 100

So, CA=10

In the 3r section we traveled 10 units.

So, in total he traveled 10 + 17 + 9 = 36 units

As every unit is 0.75 miles he traveled 36*0.75 miles:

36*0.75 = 27 miles

He traveled in total 27 miles!!