1. 13.1 The Distance Formula

2. This should not be new Y X I II III IV Origin

3. The distance between the black points A and B is found by subtracting the vertical distances and taking the absolute value. Distance always has to be positive so we always want to use the absolute value. |6- -2| or |-2-6| To find the distance between the red points C and D you subtract the horizontal distances and use the absolute value. |1-7| or |7-1| This method can only be used to find distances of vertical or horizontal segments.

4. When the line segments are not vertical or horizontal then we can use the DISTANCE FORMULA. This formula is derived from the PYTHAGOREAN THEOREM. The distance d between points (x 1,y 1 ) and (x 2,y 2 ) is given by :

5. Suppose we have the following triangle, what kind of triangle is this? What is the distances between A and B? What is the distance between B and C? What is the distance between A and C? Use the distance formula to verify your answer for the distance AC.

6. Now not every single triangle can be drawn as a right triangle, and in some instances we might be referring to some figure other than a triangle. However the distance formula is consistent for all figures. You can find the distance between any 2 points as long as you know the coordinates of those 2 points.

7. Prove that triangle ABC is isosceles, is it equilateral too?

8. A lot of the times the distance formula will be used alongside properties of certain figures. When this happens a single problem can be coupled with the use of certain properties as well as ideas of parallel and perpendicular lines (slope).

9. Determine what type of triangle ∆ABC is. Is it isosceles? Scalene? Right?

10. IDENTIFY THE TYPE OF QUADRILATERAL…FIND SLOPES AND DISTANCES FOR ALL 4 SEGMENTS