Distance Formula & Midpoint of a Segment

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Presentation transcript:

Distance Formula & Midpoint of a Segment Tutorial 12e

The Distance Formula The distance d between two points A (x1,y1) and B (x2,y2) is: (x1,y1)A B(x2,y2)

Example Distance Problem The graph shows Juan’s newspaper route. Find the distance between Parker and Commonwealth in miles. (3,2) (1,-3) (-3,-4) The distance between Parker and Commonwealth is 5.4 miles

If AM  MC, then M is the midpoint of AC. A midpoint of a segment is a point that divides a segment into two congruent segments. A M C If AM  MC, then M is the midpoint of AC.

The Midpoint Formula The coordinates of the midpoint M of AB with the endpoints A (x1,y1) and B (x1,y2) are the following: • A(x1,y1) B(x2,y2) •

Example Midpoint Problem Find the coordinate of the midpoint of segment JS. Step 1: First you must locate the coordinates of the two endpoints of segment JS. (x1,y1) (-3,2) (- 1/2, 1/2 ) • J has a coordinate of (-3,2) S has a coordinate of (2,-1) (2,-1) (x2,y2) Step 2: Substitute the coordinates into the midpoint formula, then solve. ÷ ø ö ç è æ + = 2 , 1 y x M The coordinate of the midpoint of JS is

÷ ø ö ç è æ + = 2 , 1 y x M Remember: Check your Answers

÷ ø ö ç è æ + = 2 , 1 y x M Remember:

The End Time to move on to the assignment or the next lesson