Video Transcript
James is making a map of his local
area measured in meters. The coffee shop is at negative
five, negative four, and the Italian restaurant is at zero, six. Find the distance between the
coffee shop and the Italian restaurant giving the answer to one decimal place.
We begin by sketching the
two-dimensional coordinate plane as shown. We are told that the coffee shop
lies at the point with coordinates negative five, negative four. The Italian restaurant lies at the
point with coordinates zero, six. The question asks us to find the
distance between these two points where each unit is one meter. In order to do this, we recall that
the distance 𝑑 between two points 𝑥 one, 𝑦 one and 𝑥 two, 𝑦 two is given by 𝑑
is the square root of 𝑥 two minus 𝑥 one all squared plus 𝑦 two minus 𝑦 one all
squared. We will let the coffee shop have
coordinates 𝑥 one, 𝑦 one and the Italian restaurant have coordinates 𝑥 two, 𝑦
two.
Substituting our values into the
formula, we have 𝑑 is equal to the square root of zero minus negative five all
squared plus six minus negative four all squared. This simplifies to the square root
of five squared plus 10 squared. And since five squared is 25 and 10
squared is 100, we have 𝑑 is equal to the square root of 125. We could simplify this to five root
five. However, we’re asked to give our
answer to one decimal place. Typing the square root of 125 into
our calculator gives us 11.1803 and so on, which is 11.2 to one decimal place. We can therefore conclude that the
distance between the coffee shop and the Italian restaurant is 11.2 meters.
