Question

The mayor of a town places a map of the town on a coordinate grid with Town Hall at the point (0,0) and with each unit representing a mile. Smithville is at the point (-25,10) and Jones City is at (15,12). It costs $0.18 a mile to drive a car. How much does it cost to drive from Smithville and Jones City?

Answer 1

Given that the question rightly asks the amount it cost to drive from Smithville to Jones City, we have;

The question rightly asks the amount it cost to drive from Smithville to Jones City is approximately $7.209

Explanation:

The coordinates of Smithville is (-25, 10)

The coordinates of Jones City is (15, 12)

The cost of driving a car for a mile = $0.18

Therefore, the distance from Smithville to Jones City is given by the formula for the distance, l, between two points with coordinates as follows;

`l = \sqrt{\left (y_(2)-y_(1) \right )^(2)+\left (x_(2)-x_(1) \right )^(2)}`

Where;

(x₁, y₁) = (-25, 10) and (x₂, y₂) = (15, 12)

`l = \sqrt{\left (12-10 \right )^(2)+\left (15-(-25) \right )^(2)} = 2 \cdot √(401)`

The distance from Smithville to Jones City = 2·√401 ≈ 40.05 miles

The amount, A, it cost to drive from Smithville to Jones City a distance of approximately 40.05 miles is therefore given as follows;

A = 40.05 miles × $0.18 ≈ $7.209