Download Warm-up

Warm-up
1. D is between B and E. ED = x, BD = 30
and EB = 4x + 6. Find ED and EB.
2. E bisects segment DF. DE = 2x, and
EF = 8x – 3. Find DE, EF, and DF.
Discovering the Midpoint Formula
What do you think a midpoint is? Write
down a quick definition and discuss it
with your partner.
Which point do you think
is the midpoint in the
picture to the right?
How do you know for sure
it’s the midpoint?
What if the red marks were not there?
Would you know for sure it was still a midpoint?
Discovering the Midpoint Formula
So, M is the midpoint. What if the points were on a
number line? P was located at 2 and Q was located at
8. Where would M be located?
P
M
Q
How did you know where M was located?
How can you use math to find out M’s location?
Some people may have just counted to find M,
But what if the numbers were so big, it was hard to
count….
Discovering the Midpoint Formula
If M was still a midpoint, how could we use math to find
it’s location now?
P
-35
-1
M
33
Q
67
101
If you are still stuck, let’s relate it to your grades. Say
you got a 90 on one paper and a 70 on another paper.
What would your final grade be?
How did you use your math to get your final grade?
Could you use this same idea to find M?
135
Discovering the Midpoint Formula
Everything we have dealt with was 1-dimensional; we
were using a number line. What if we moved to 2-D?
How would we find a midpoint on a coordinate plane
without counting?
If you are stuck,
(4, 10)
estimate where you
think the midpoint is.

y







Did you get (-2, 1)?



  














(-8, -8)





(-2, 1)





x







How can you use
math to get these
coordinates?
Discovering the Midpoint Formula
Just
AVERAGE!!!

Average your x values:
8  4
 2
2
y
Then average your
y values:
(4, 10)










  














(-8, -8)





(-2, 1)





x







8  10
1
2
ANSWER: (-2, 1)
Midpoint Formula
• (The average of the x’s and the average of the
y’s)
x1  x2 y1  y2
(
,
)
2
2
Examples:
Find the coordinates of the midpoint of
each segment:
1. (-8,5) and (3,-6)
2. (4,6) and (6,4)
3. (8,6) and (22,20)
On your own.
4. (0,5) and (6,7)
5. (1,-4) and (9,3)
6. (6,0) and (3,5)
Discovering the Midpoint Formula
One endpoint of a segment is (-2, 8). The midpoint is
(4, -1). What are the coordinates of the other endpoint?

y


(-2, 8)








  























(4, -1)





x



Example:
M is the midpoint of AB . A has the coordinates
(2,2) and M has the coordinates (4,-3). Find the
coordinates of B.
Extra Examples:
M is the midpoint of XY . X has coordinates (2,7)
and M has coordinates (6,1). Find the
coordinates of Y.
S is the midpoint of RT. R has coordinates (-6,-1),
and S has coordinates (-1,1). Find the
coordinates of T.