MIDPOINT FORMULA

MATH 10DAISYREE JEAN R. MEDINO

Give the difference in each pair of integers
then divide by 2.
1. -8 and - 10
2. 12 and - 17
3. -24 and 14
4. 7 and -19
5. 21 and 15
1
14.5
-19
13
3

A plane flying between
two cities cannot stop
mid-air to ascertain its
position. If you are the
pilot and the plane gets
some engine damage,
will you go back or
head on to the final
destination? What
factor would you
consider in making a
decision?
A plane has a GPS
Navigation System that
gives the coordinates
and determines the
distance it travels. If the
plane had already
passed halfway through
its flight distance, it’s
better to continue flying
towards its final
destination. If not, then
turn back.

Learning Competency 27: Derives the
distance formula.
OBJECTIVES
a. Determine the coordinates of the
midpoint of a line segment on a coordinate
plane using the midpoint formula.
b. Find the other endpoint of a line segment
when the midpoint and one endpoint are
given.
c. Appreciate the importance of the midpoint
formula in making wise decisions.

P and Q are
endpoints of a
line segment.
Point M is called
the midpoint and it
divides line
segment PQ into
two equal parts.
The x-coordinate of M is
the average of the x-
coordinates of P and Q,
while the y-coordinate of
M is the average of the
y-coordinates of P and
Q.

Illustrative Example 1:
The coordinates of the endpoints of AB̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ are
(1, -5) and (7, 4) respectively. What are the
coordinates of its midpoint M?
Solution: Let 𝑥1= 1, 𝑦1 = -5, 𝑥2 = 7, and 𝑦2 =4
Substitute these values in the midpoint formula
The coordinates of the
midpoint of AB̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ are (4,−12).

If P (-1, 2) is the midpoint of RJ̅̅̅̅, and one endpoint R
has coordinates (7, -8), find the coordinates of the
other endpoint J.
Solution: Let x = -1, y = 2, 𝑥1 = 7, and 𝑦1 = -8
Substitute these values in the midpoint formula
Equate the coordinates, then solve.
The coordinates of the other endpoint J are (-9, 12).

Strike and Chezka are having their
vacation in two different islands in the
Philippines as illustrated below. They
decided to meet at a point halfway
between their locations to save travel
time. Find the exact coordinates of the
midpoint between the two islands
where they will meet.
Solution:
Let 𝑥1 = -3, 𝑦1 = 1,
𝑥2 = 2, and 𝑦2 = -1
Substitute these values
in the midpoint formula
The coordinates of the
midpoint between the two
islands are ( −12 ,0).

Name the endpoints of the given line
segment.
Name the point on line segment PQ that
divides it into two equal parts.
What is the relation of the x-coordinate of
M with the x-coordinates of P and Q? How
about their y-coordinates?
How do you determine the coordinates of
the midpoint of a line segment?

Supply the missing parts of the solution.
1. Find the midpoint M of a line segment
whose endpoints are A (-3, 5) and F (6, 1).

2. The midpoint of a line segment is (4, 7). If
one endpoint is (-6, 9), what is the other
endpoint?

SEAT WORK #2
ANSWER ON YOUR NOTEBOOK!

A. Find the midpoint of the line segment with the given
endpoints.
1. P (-1, -6) and R (-6, 5)
2. W (-1.2, 1.0) and A (5.2, -5.3)
3. C (2, -1) and T (-6, 0)
B. Find the other endpoint of the line segment with the
given endpoint and midpoint.
1. Endpoint: (2, 5)
Midpoint: (5, 1)
2. Endpoint: (-1, 9)
Midpoint: (-9, -10)

The Midpoint Formula is a formula that
can be used to find the coordinates of the
midpoint of a line segment on the
coordinate plane.
WHAT IS MIDPOINT FORMULA?
WHAT IS THE MIDPOINT FORMULA?

WORKSHEET #1
ANSWER ON YOUR NOTEBOOK!

Solve the following problems by using the midpoint formula.
1. Sheena and her friend Ryan would like to work on their
math project. They decided to meet each other at a point
halfway between their houses with coordinates (-14, 60) and
(2,100) respectively. Should they meet in the park
represented by the coordinates (-8, 70)? Or in the coffee
shop represented by the coordinates (-6, 80)? Justify your
answer.
2. While designing his garden, Raymond created a grid
representing his backyard. He already has one lamp post in
the garden at coordinates (6, 20). He wants to add another
one so that the center of the fishpond which is at coordinates
(5, -10) would be the midpoint of the two lamp posts. Where
should the second lamp post be placed?

1. Which of the following would give the
coordinates of the midpoint of P(-6,13)
and Q(9,6)?
DIRECTIONS: Read and understand the
questions and write the letter together
with its choices.

2. The endpoints of a segment are (-5,2)
and (9,12), respectively. What are the
coordinates of its midpoint?
with its choices.
A.(7,5)
B. (2,7)
C. (-7,5)
D. (7,2)

3. Find the midpoint of the line segment
with these endpoints: (4,6), (9,3)
with its choices.
A.(6.5, 4.5)
B. (14, 0)
C. (5,6)
D. (-2.5, 1.5)

4. Find the coordinates of the midpoint
of the segment whose endpoints are H(8,
2) and K(6, 10).
with its choices.
A. (14, 12)
B. (1, 4)
C. (7, 6)
D. (2, 8)

5. Find the midpoint of the segment.
with its choices.
A. (–3, –1)
B. (–2, 0)
C. (–2, –1)
D. (–3, 0)

EXCHANGE PAPERS
Write corrected by

Use the midpoint formula to solve the following
1. Which of the following pairs of points have a midpoint
with coordinates (0, 0)?
A. (1, 1) and (-1, 0) B. (-3, 0) and (3, 0)
2. Find the midpoint between (1.53, -0.2) and (-1.33,
2.0).
3. Given the endpoint (2, 8) and midpoint (4, 4), what is
the other endpoint?
4. While on a hunting trip Jose created a map grid. He
determined that a mountain could have the coordinates
(425, 1800) and that his current position is at (173, 254).
If a nipa hut is located exactly midway between Jose
and the mountain, what coordinates should represent
the nipa hut’s location?
(0.01, 0.9)
(6, 0)
(299, 1027)

MIDPOINT FORMULA

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to MIDPOINT FORMULA

Similar to MIDPOINT FORMULA (20)

Recently uploaded

Recently uploaded (20)

MIDPOINT FORMULA