Honors Geometry
1.3 DISTANCE AND MIDPOINTS
Do Now:
Do Now:
 What is the distance between the following two
points in a coordinate plane?
5, −3 𝑎𝑛𝑑 3, 9 ?
8, −8 , 2, −12 ?
Homework
 Questions?
 Confusions?
 Concerns?
 ASK ASK ASK!
Definition:
 Distance: The distance between two points is the
length of the segment with those points as its
endpoints.
Example One
 Distance between
 0 and 5 ?

1 and 4 ?

-5 and -3 ?

-5 and 4?
Distance Formula (for a number line)
Example Two:
But…..
 What happens if we try to find the distance in a
coordinate plane?
Example Three
 Find the distance between (-4, -5), and (5, - 1)
Distance Formula (for a coordinate plane)
Example Four
 Determine the distance between (-5, 6) and (8, -4)
You Try!
 Determine the distance between (4, 3) and (-3, -7)
Definition
 Midpoint: The midpoint of a segment is the point
halfway between the endpoints of the segment. (i.e.
in the middle of the entire segment)
Example Five
 Determine the midpoints of
0 and 4
-5 and -3
-4 and 2
Midpoint Formula (on a number line)
If the endpoints of the line are at x1 and x2… the
midpoint of the line is….
Example Six
 Determine the midpoint of each segment
BUT….
 What happens if we put it in a coordinate plane?
Example Seven
 Determine the midpoint of ST if S(-6, 3), and T(1, 0)
Definition
 Midpoint in a coordinate plane:
𝑥1 + 𝑥2 𝑦1 + 𝑦2
,
2
2
Example Eight:
 Find the coordinates of the segment with A(5, -3)
and B(-4, 7)
You Try!
 What’s the midpoint of (-7, -2) and (5, 1)? What’s the
distance?
Example Nine:
 Slightly Different way to phrase it: The midpoint of
CD is M(-2, 1). One endpoint is C(-5, 7). What are
the coordinates of the other endpoint D?
Example Ten
 The midpoint of AB has coordinates (4, -7).
Endpoint A has coordinates (-3, -5). What are the
coordinates of B?
You Try!
 Determine the coordinate of G if the midpoint of EG
is P and E(-8, 6) and P(-5, 10)
Definition
 Segment Bisector: Any segment, line or plane that
intersects a segment at its midpoint is called a
segment bisector.
Example Eleven
 AB and CD intersect at point Q. AB bisects CD. If
CQ=11x+3 and QD=135, what is x?
Example Twelve
 AB and CD intersect at point Q. AB bisects CD. If
CQ=5x and CD=70, what is x?
You Try!
 If AB is bisected by DE such that AB intersects DE at
point F, determine x if

AF = 2x + 1 and BF = 5x – 8

AF = 6x – 9 and AB = 87
Practice Problems
 Try some on your own/in small groups
 As always don’t hestitate to ask questions if you are
confused
Exit Ticket
 What is the distance of a line with endpoints (-2, 5)
and (8, -3)? Leave it as a square root (don’t write it
as a decimal)
 What is the midpoint of the same line?