Discovering a Formula for Distance
1. Plot the points A(1, 1) and B(4, 6) on a piece of graph paper and connect them with a straight line
(use a ruler!)
2. Draw a straight line down from point B and a straight line to the right from point A. Keep drawing
each line until the two lines intersect each other. Label that the intersection point C. What is the
ordered pair for point C? What shape did you just create?
3. If the two lines you drew in #2 are the legs of a triangle, what is the line that connects points A and
B called??
4. What formula could you use to find the length of the line between points A and B? Find the
distance.
5. Let’s say you didn’t have the picture of the triangle to look at. How could we find the distance
between point A and point C if we couldn’t count the distance? How could we find the distance
between point B and point C if we couldn’t count the distance?