Using the Distance Formula

Q:  The community of A is laid out using a rectangular coordinate system where the distance between consecutive whole grid marks represent 1 km.  If the landmark of B is centered at (-3, 3/2) while the landmark of C is centered at (5/2, 7), how far apart are the landmarks B and C from each other?

A:  We are basically asked to find the distance between the points (-3, 3/2) and (5/2, 7).  We can do this using the distance formula, which gives us the distance between 2 points:

d = √( (x₂ – x₁)² + (y₂ – y₁)² )

So, we can plug in our x and y points like so:

d = √( (5/2 – (-3) )² + (7 – 3/2)² ) = √( (5/2 + 3 )² + (7 – 3/2)² )

= √( (11/2)² + (11/2)² )

= √( 121/4 + 121/4 )

= √(242/4)

= 11 √(2) / 2 ≈ 7.78 km