WORD PROBLEM:
You want to pay your tuition fee for this coming September Monthly Summative Test
and as you are directed to the Business office, which path would you choose to go to
have a short cut? Short cut by means of going to the business office in short span of
time. Show it by computing the sum of the distance of AB and BC as path A, and the
distance of AC as path B. To which path will you prefer and why? You prove your
answer by showing all your solutions. Incase of decimals, round it to two decimal
places. Express the distance in meters.
(1, 4)
C
B
(0, 0)
A
(8, 0)
This pandemic Ramon wants to share his blessings by
visiting Fatima’s family and give packs of groceries. To
further check, he wants to know as to how many
kilometers from Richard’s house to Fatima’s house in
order for him to prepare extra gasoline. On his
references, he knows that Fatima is living in Lagtang
and that Barangay Lagtang is mapped on a
Coordinate Grid with the origin being at the Barangay
Hall. Richard’s House is located at the point (-5,7)
while Fatima’s House is located at (2,-3). Ramon is
now estimating the distance as how far is Fatima’s
house from Richard’s House.
Questions:
(-5,7)
Fatima
Richard
(2,-3)
1.What do you think
should Ramon do in
order for him to know
or estimate the
distance from
Richard’s house to
Fatima’s house?
Learning Targets




1. Derive the distance formula using the Pythagorean
theorem.
2. Solve the distance between two points by applying
the distance formula.
3. Apply the distance formula in finding lengths of
segments.
4. Solve problems that are application of the distance
formula.
DRILLS:
a. CD = 7
b. XY = 5
c. RS = 7
Hook-up activity:
 What is the distance from points
A to B?
 What is the distance from points
B to A?
5 units
5 units
 What is the distance from Points
E to F? What about F to E?
4 units
DRILLS:
 What is the distance from points A to B?
or /AB/= /0 - 5/= /-5/ = 5
5 units
Key words: difference, absolute value, coordinates
The distance/absolute value between two points is
the absolute value of the difference of their
coordinates.
K
ESSENTIAL QUESTIONS



How is the Distance Formula being
derived geometrically?
Which Right Triangle theorem is being
used in the derivation?
In what way the skills in solving the
Distance between two points has its
significance in real-life?
DRILLS:
a. CD = 7
b. XY = 5
c. RS = 7
K
NORTH
EAST
WEST
SOUTH
WORD PROBLEM:
You want to pay your tuition fee for this coming September Monthly Summative Test
and as you are directed to the Business office, which path would you choose to go to
have a short cut? Short cut by means of going to the business office in short span of
time. Show it by computing the sum of the distance of AB and BC as path A, and the
distance of AC as path B. To which path will you prefer and why? You prove your
answer by showing all your solutions. Incase of decimals, round it to two decimal
places. Express the distance in meters.
(1, 4)
C
B
(0, 0)
A
(8, 0)
THE MIDPOINT FORMULA