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?
a.5 milesB)7 milesC)9 milesD)11 milesE)13 miles

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.