1. LEARNING PLAN IN MATHEMATICS
INSTRUCTIONAL SEQUENCES
I. Objectives:
At the end of the discussion, the students with at least 85% of mastery will be able to:
a. State the distance formula
b. Solve the value of distance between two points by the use of distance formula
c. Construct a graphical representation of the distance formula by forming a right triangle
from any given two points and using this representation to find the length between two
points
d. Understand the connection between Pythagorean Theorem and Distance Formula
e. Show enthusiasm during class discussion.
II. Subject Matter
a. Topic: Distance Formula
b. Reference: Benes, Salita (2008). Painless Math Geometry. Anvil Publishing Inc.
pp. 118-119
III. Procedures:
Daily Routine
 Prayer
 Checking of Attendance
Teacher’s Activity
A. Activity
Before we proceed to our lesson proper for
the day. Let’s have an activity.
Plot these coordinates on our Cartesian
plane.
 (3,2)
 (8,7)
 (8,2)
Who wants to plot the coordinates?
Students’ Activity
(3,2)
(8,7)
(8,2)

2. Very Good!
Who wants to name the points?
Very good. Now who wants to connect the
points?
Very good class! What figure did we form?
Exactly.
How do you know to use this theorem?
What problems do you have using this?
B. Analysis
Based on our activity, what do you call the
̅퐴̅̅퐵̅ in the right triangle?
Very good!
How about ̅퐴̅̅퐶̅ and ̅퐵̅̅퐶̅? What do you call
these line segments?
Very good!
From the figure in the activity, how can we
get the length of ̅퐴̅̅퐶̅?
A right triangle!
The intersection made it a right triangle.
Hypotenuse!
There is no given length of each sides.
Sides of the right triangle!
Since ̅퐴̅̅퐶̅ is plotted on the x- axis, we have
to get the difference between x2 and x1.
x2=8, x1=3
x2-x1
= 8-3
= 5
(3,2)
(8,7)
(8,2)
A
B
(3,2) C
(8,7)
(8,2)
A
B
C

3. Who wants to solve on the board?
Very good!
How about ̅퐵̅̅퐶̅? How can we get the length of
̅퐵̅̅퐶̅?
Who wants to solve on the board?
Very Good!
From the computations that we did, using
what kind theorem we are going to use to find
the length of ̅퐴̅̅퐵̅ ?
Great!
Who can remember the Pythagorean Theorem
formula and what is it?
Therefore, to find the length of ̅퐴̅̅퐵̅, we let
̅퐴̅̅퐵̅ = 퐷 and D is the hypotenuse of the right
triangle, ̅퐵̅̅퐶̅ = b and ̅퐴̅̅퐶̅ = a. It is also the same
as:
̅퐵̅̅퐶̅ = y2 – y1
̅퐴̅̅퐶̅ = x2 – x1
̅퐴̅̅퐵̅ = ?
Great Job! And now, who wants to substitute
the equivalent of a and b to the distance
formula that we derive?
Very Good! And now we have the distance
formula. Through substitution method, who
wants to substitute the value that we get from
our previous activity?
Since ̅퐵̅̅퐶̅ is plotted on the y-axis, we have to
get the difference between y2 and y1.
y2=7, y1=2
y2 – y1
= 7-2
= 5
Sir, we are going to perform the Pythagorean
Theorem.
The Pythagorean formula is
c2 = a2 + b2
√푐2 = √푎2 + 푏2
c = √푎2 + 푏2
Thus,
퐷2 = 푎2 + 푏2
√퐷2 = √푎2 + 푏2
퐷 = √푎2 + 푏2
퐷2 = √(푥2 − 푥1)2 + (푦2 − 푦1 )2
We come up with, a = 5, b = 5
By substitution: 퐷 = √푎2 + 푏2
퐷 = √(5)2 + (5)2
퐷 = √50

4. C. Abstraction
Again what is the distance formula?
Very Good!
What is the connection between Pythagorean
Theorem and Distance Formula?
D. Application
We are having an activity, first, group yourself
into 3. And answer the given problem sets.
Graph and show that the following coordinates
forms an isosceles triangle by using the
distance formula.
S (-1,4)
C (0,1)
B (2,5)
You are given 10 minutes to answer it with
your partners.
The Distance Formula is
퐷2 = √(푥2 − 푥1)2 + (푦2 − 푦1 )2
The Pythagorean Theorem States that
c2 = a2+b2
Where C is the length of the hypotenuse, a is
the length of the horizontal leg, b is the length
of the vertical leg.
The Distance formula states that
퐷2 = √(푥2 − 푥1)2 + (푦2 − 푦1 )2
Where D is the Distance between two points ,
(푥2 − 푥1) is the horizontal distance between
two points and (푦2 − 푦1 ) is the vertical
distance between two points.
B(2,5)
S (-1,4)
C (0,1)

5. IV. Evaluation
GROUP I
̅푆̅̅퐶̅ = √(푥2− 푥1)2 + (푦2 − 푦1 )2
=√(−1 − 0)2 + (−4 − 1)2
=√(−1)2 + (−3)2
=√1 + 9
= √10
GROUP II
̅퐶̅̅퐵̅ = √(푥2 − 푥1)2 + (푦2 − 푦1 )2
=√(2 − 0)2 + (5−1)2
=√4 + 16
=√20
GROUP III
̅푆̅̅퐶̅ = √(푥2− 푥1)2 + (푦2 − 푦1 )2
=√(2 + 1)2 + (5+4)2
=√10
Get ½ crosswise sheet of pad paper and answer the following.
Find the distance between the given points.
1. (0,9) and (0,13)
2. (4,5) and (-3,5)
3. (8,1) and (8,-2)
4. (1,0) and (5,2)
5. (5,-4) and (1,-1)
V. Closure
In your assignment notebook, answer the following:
A. Graph and Find the distance using distance formula.
I (-4,6)
V (2,5)
Y (-1,6)
S (5, 10)
B. Make a research on midpoint and give at least 2 examples.