Las Math g10 q2 Melc9 w7

10
Mathematics
Learning Activity Sheet
Quarter 2 – MELC 9
Week 7
Applying the Distance Formula to Prove some
Geometric Properties
REGION VI – WESTERN VISAYAS

Mathematics 10
Activity Sheet No. 10
First Edition, 2020
Published in the Philippines

By the Department of Education
Region 6 – Western Visayas
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royalties.
This Learning Activity Sheet is developed by DepEd Region 6 – Western Visayas.
ALL RIGHTS RESERVED. No part of this learning resource may be reproduced or

transmitted in any form or by any means electronic or mechanical without written permission
from the DepEd Regional Office 6 – Western Visayas.
Development Team of Activity Sheet
Writers: Genie G. Rimpillo, Elena C. Gelloagan, Kirleen M. Inapan and

Marjolene Galamiton
Illustrator: Angeline Joy F. Jarangue
Editor: Rowena S. Carillo
Layout Artist: Felizardo S. Valdez III
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Jenny Anne L. Gange
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Elleda E. De la Cruz
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Ma. Gemma M. Ledesma
Josilyn S. Solana
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Introductory Message
Welcome to Mathematics 10!
The Mathematics Learning Activity Sheet is a product of the

collaborative efforts of the Schools Division of Guimaras and DepEd
Regional Office VI - Western Visayas through the Curriculum and Learning
Management Division (CLMD). This is developed to guide the learning
facilitators (teachers, parents and responsible adults) in helping the learners
meet the standards set by the K to 12 Basic Education Curriculum.
The Mathematics Learning Activity Sheet is self-directed

instructional materials aimed to guide the learners in accomplishing
activities at their own pace and time using the contextualized resources in
the community. This will also assist the learners in acquiring the lifelong
learning skills, knowledge and attitudes for productivity and employment.
For learning facilitator:
The Mathematics 10 Learning Activity Sheet will help you facilitate the
teaching-learning activities specified in each Most Essential Learning Competency
(MELC) with minimal or no face-to-face encounter between you and learner. This
will be made available to the learners with the references/links to ease the
independent learning.
For the learner:
The Mathematics 10 Learning Activity Sheet is developed to help you

continue learning even if you are not in school. This learning material provides you
with meaningful and engaging activities for independent learning. Being an active
learner, carefully read and understand the instructions then perform the activities
and answer the assessments. This will be returned to your facilitator on the agreed
schedule.
ii
Quarter 2, Week 7
Learning Activity Sheets (LAS) No. 10

Name of Learner: Grade and Section:
School: Date:
Applying the Distance Formula to Prove

Geometric Properties
I. Learning Competency with Code
Apply the distance formula to prove some geometric properties
(M10GE- IIg – 2)
II. Background Information for Learners

Your knowledge and skills on the different mathematical concepts
previously learned in performing mathematical operations are of great
help in understanding this lesson especially the distance formula and its
application in proving some geometric properties.
As you go through this lesson, you will learn how distance formula,
midpoint formula, and coordinate proof help you find solutions to real-
life problems and make wise decisions.
Here are the steps in developing geometric proof:
1. Plot the points, connect the points to form a figure then label.
2. Determine the formula.
3. Show the solutions.
4. Make a conclusion.
Example:
Given: ABC with A(-1,4), B(1,-2) and C(-3,-2)
Show: ABC is an isosceles triangle.
1. Plot the points, connect the points to form a figure then label.
1
2. Determine the formula.
Use the Distance Formula:
𝐷 = √(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2
3. Show the solutions. (Using Distance Formula)
a) A ( -1,4), and B (1,-2)
𝐴𝐵 = √(−1 − 1 )2 + (4 + 2 )2
𝐴𝐵 = √( −2)2 + (6 )2
𝐴𝐵 = √4 + 36
𝑨𝑩 = √𝟒𝟎
b) A ( -1,4), and C (-3,-2)
𝐴𝐶 = √(−1 + 3 )2 + (4 + 2 )2
𝐴𝐶 = √( 2)2 + (6 )2
𝐴𝐶 = √4 + 36
𝑨𝑪 = √𝟒𝟎
c) AC = AB implies that AC AB
4. Make a conclusion.
Therefore, the triangle is isosceles because it has two congruent
sides.
III. Accompanying DepEd Textbook and

Educational Sites
Melvin M. Callanta, et.al., 2015. Mathematics 10 Learner’s Module,

First Edition, Rex Book Store, Inc. pp. 234 -244.
2
III. Activity Proper
Activity 1
A. To further understand the lesson, read the topics indicated in the

table below which are found in your Mathematics 10 Learner’s
Module. These topics will guide you in proving some geometric
properties.
Topics Page/s
If P and Q are two points, then the distance

Distance between 234
from P to Q is the same as the distance from
Two Points
Q to P. That is, PQ = QP.
Distance Formula 2
d = √(𝑥1− 𝑥2) + ( 𝑦1−𝑦2)
2 235
𝑥1 + 𝑥2) 𝑦1 + 𝑦2)
Midpoint Formula Mp = ( , ) 238
2 2
A proof that uses figures on a coordinate 239 - 240

Coordinate Proof
plane to prove geometric properties.
B. Apply the key concepts of the distance formula including the

midpoint formula, and the coordinate proof in answering Activity 8,
entitled, “I Missed You, But Now I found You! “in Mathematics 10
Learner’s Module on pages 243 - 244. Use a separate sheet of
paper for your answers.
Activity 2
A. Direction: Write the coordinate proof to prove the following geometric

properties. Use a separate sheet of paper for your answers.
1. Given: DEF with D( -1,3), E (5,3) and F(2,-3)

Show: DEF is not an equilateral triangle.
2. Given: A(3,3), B(6,-1),C(2,0),D(-3,-1),E(1,2),F(0,-2)

Show: ABC DEF
3. Triangle ABC has vertices A(2,1), B (4,5), and C(7,1). Calculate

the perimeter of the triangle ABC.
3
Activity 3
To summarize what you have learned in this lesson, answer the question
below:
How do you prove some geometric properties using distance formula?
IV. Reflection
In this lesson, I learned that
V. Answer Key
Activity 1B
VI. Links and/or Other References

For additional Activities and information, you may visit the following links:
https://www.whiteplainspublicschools.org/cms/lib5/NY01000029/Centricity/
Domain/360/Coordinate%20Geometry%20Proofs%20Packet%202012.pdf
https://www.onlinemathlearning.com/coordinate-proof-hsg-gpe4.html

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10

REGION VI – WESTERN VISAYAS

Published in the Philippines

This Learning Activity Sheet is developed by DepEd Region 6 – Western Visayas.

ALL RIGHTS RESERVED. No part of this learning resource may be reproduced or

Development Team of Activity Sheet

Writers: Genie G. Rimpillo, Elena C. Gelloagan, Kirleen M. Inapan and

The Mathematics Learning Activity Sheet is a product of the

The Mathematics Learning Activity Sheet is self-directed

For learning facilitator:

For the learner:

The Mathematics 10 Learning Activity Sheet is developed to help you

Learning Activity Sheets (LAS) No. 10

Applying the Distance Formula to Prove

II. Background Information for Learners

b) A ( -1,4), and C (-3,-2)

III. Accompanying DepEd Textbook and

Melvin M. Callanta, et.al., 2015. Mathematics 10 Learner’s Module,

A. To further understand the lesson, read the topics indicated in the

If P and Q are two points, then the distance

A proof that uses figures on a coordinate 239 - 240

B. Apply the key concepts of the distance formula including the

A. Direction: Write the coordinate proof to prove the following geometric

1. Given: DEF with D( -1,3), E (5,3) and F(2,-3)

2. Given: A(3,3), B(6,-1),C(2,0),D(-3,-1),E(1,2),F(0,-2)

3. Triangle ABC has vertices A(2,1), B (4,5), and C(7,1). Calculate

How do you prove some geometric properties using distance formula?

VI. Links and/or Other References

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