Question

A ship sails from point (1, 2) to point (5, 5), as shown. If each unit represents one mile, how far has the ship sailed?

Answer 1

Hello!

To find how far the ship has sailed, we need to use the distance formula. The distance formula is: $d = \sqrt{(x_{2}-x_{1}) ^{2}+ (y_{2}-y_{1}) ^{2} }$.

Before using the formula, we need to assign the given points to $(x_{1}, y_{1})$ and $(x_{2},y_{2})$. The point (1, 2) can be assigned to $(x_{1}, y_{1})$ and (5, 5) can be assigned to $(x_{2},y_{2})$.

With the assigned ordered pairs, we can substitute it into the formula.

$d = \sqrt{(5-1) ^{2}+ (5-2) ^{2} }$

$d= \sqrt{(4) ^{2}+ (3) ^{2} }$

$d = \sqrt{16 + 9}$

$d = \sqrt{25} = 5$

Given that each unit represents one mile, then therefore the ship has sailed 5 miles, which is choice A.