Question

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:

The distance between two points (
`x_(1),y_(1)`) and (
`x_(2),y_(2)`) on the coordinate plane are given by the formula

`\sqrt{(x_(2) - x_(1))^(2) + (y_(2) - y_(1))^(2)  }`

Therefore, the distance between points (12,6) and (12,15) is
`\sqrt{(12 - 12)^(2) + (15 - 6)^(2)} = 9` units

Again, the distance between the points (12,15) and (4,0) is
`\sqrt{(4 - 12)^(2) + (0 - 15)^(2)} = 17` units

And the dictance between the points (4,0) and (12,6) is
`\sqrt{(12 - 4)^(2) + (6 - 0)^(2)} = 10` units

Therefore, the total distance is (9 + 17 + 10) = 36 units.

If each unit on the coordinate plane represents 0.75 miles, then Tony rides on the city bus by (36 × 0.75) =27 miles. (Answer)