Transcript Chapter 1.3 Notes: Use Midpoint and Distance Formulas

Chapter 1.3 Notes: Use Midpoint
and Distance Formulas
Goal: You will find lengths of segments in the
coordinate plane.
• Midpoints and Bisectors:
• The midpoint of a segment is the point that divides
the segment into two congruent segments.
• A segment bisector is a point, ray, line, line
segment, or plane that intersects the segment at its
midpoint.
• A midpoint or a segment bisector bisects a
segment.
Ex.1: In the skateboard design, VW bisects XY at
point T, and XT = 39.9 cm. Find XY.
Ex.2: Point M is the midpoint of VW . Find the length
of VM .
Ex.3: Identify the segment bisector of PQ . Then
find PQ.
• To find the midpoint using coordinates in a
coordinate plane, you will use the Midpoint
Formula.
• The Midpoint Formula:
• If A(x1, y1) and B(x2, y2) are points in a coordinate
plane, then the midpoint M of AB has coordinates
– Midpoint =
 x1  x2 y1  y2 
,


2 
 2
Ex.4: The endpoints of RS are R(1, -3) and S(4, 2). Find
the coordinates of the midpoint M.
Ex.5: The midpoint of JK is M(2, 1). One endpoint is
J(1, 4). Find the coordinates of endpoint K.
Ex.6: The endpoints of GH are G(7, -2) and H(-5, -6).
Find the coordinates of the midpoint P.
Ex.7: The midpoint of AB is M(5, 8). One endpoint is
A(2, -3). Find the coordinates of endpoint B.
• Distance Formula:
• To find the distance between two points, you will
always use the Distance Formula.
• The Distance Formula:
If A(x1, y1) and B(x2, y2) are points in a coordinate
plane, then the distance between A and B is
distance (d) =
( x2  x1 )  ( y2  y1 )
2
2
Ex.8: What is the approximate length of RS with
endpoints R(2, 3) and S(4, -1)?
Ex.9: What is the approximate length of AB with
endpoints A(-3, 2) and B(1, -4)?
Ex.10: What is the difference between these three
symbols: =,  , and ≈?