The Distance and Midpoint Formulas (1-3)

1
The Distance and Midpoint Formulas (1-3)

• Objective Find the distance between two points
  and find the midpoint of a segment.

2
Distance Formula

• Used to find the distance between two points

3
Example

• Find the distance between A(4,8) and B(1,12)

A (4, 8)
B (1, 12)
4
YOU TRY!!

• Find the distance between
• A. (2, 7) and (11, 9)
• B. (-5, 8) and (2, - 4)

5
Midpoint Formula

• Used to find the center of a line segment

6
Example

• Find the midpoint between A(4,8) and B(1,12)

A (4, 8)
B (1, 12)
7
YOU TRY!!

• Find the midpoint between
• A) (2, 7) and (14, 9)
• B) (-5, 8) and (2, - 4)

8
Find the coordinates of an Endpoint

• Example Find the coordinates of X if Y(-2,2) is
  the midpoint and Z has coordinates (2,8).
• Let Z be ( )?(2,8) in the Midpoint
  Formula.
• Write the two equations to find the coordinates
  of X.
• -2 x1 2
• 2
• 2 -2 2 x1 2
• 2
• -4 x1 2
• -2 -2 -6 x1

9

• 2 y1 8
• 2
• 2 2 2 y1 8
• 2
• 4 y1 8
• -8 -8
• -4 y1
• The solution is (-6, -4).

10
YOU TRY!

• Find the coordinates of the missing endpoint
  given that S is the midpoint of segment RT.
• T(-4, 3), S(-1, 5)?(Midpoint)