Geometry CP
1.3 Midpoint and Distance Formulas
Name:______________________________________ Date:________________ Block:_______________
Objective: Find lengths of segments in the coordinate plane.
Midpoint:_____________________________________________________________________________________
M is the midpoint of _________
So, ______________________ and _______________________
Segment Bisector:
______________________________________________________________________________________
___________ is the segment bisector of _________.
So, ______________________________________________.
Geometry CP
1.3 Midpoint and Distance Formulas
On a number line: the coordinates of the midpoint (middle) of a segment whose
endpoints have coordinates a and b is :
Example: Find the midpoint of
a. SY
b. TB
Example 1:
Example 2: Draw a picture and show all steps.
The midpoint, M of
is the point between P and Q such that PM = MQ
Find QM if PM = 5x – 2 MQ = 3x + 8
Geometry CP
1.3 Midpoint and Distance Formulas
Example 3:
The Midpoint Formula:
Example using Midpoint Formula in Coordinate Plane:
Geometry CP
1.3 Midpoint and Distance Formulas
The Distance Formula:
The distance d between any two points with coordinates (x1, y1) and (x2, y2) is
given by the formula:
Example Using Distance Formula:
a. Find the distance
M (7, 11) and E ( – 1, 5)
b. Using the distance formula, find the distance between J(9, – 5) K(– 6, 12)