Table Of ContentCLASS
X
CBSE-i UNIT-6
CORE
Coordinate
Geometry
and
Transformations
CLASS
X
UNIT-6
CBSE-i
Coordinate Geometry
and
Transformations
Shiksha Kendra, 2, Community Centre, Preet Vihar, Delhi-110 092 India
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The Curriculum initiated by Central Board of Secondary Education -International (CBSE-i) is a progressive step in making
the educational content and methodology more sensitive and responsive to the global needs. It signifies the emergence of a
fresh thought process in imparting a curriculum which would restore the independence of the learner to pursue the
learning process in harmony with the existing personal, social and cultural ethos.
The Central Board of Secondary Education has been providing support to the academic needs of the learners worldwide. It
has about 11500 schools affiliated to it and over 158 schools situated in more than 23 countries. The Board has always been
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The International Curriculum being designed by CBSE-i, has been visualized and developed with these requirements in
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The recent scientific and technological advances have thrown open the gateways of knowledge at an astonishing pace. The
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The CBSE has introduced the CBSE-i curriculum in schools affiliated to CBSE at the international level in 2010 and is now
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of this part or the core of the curriculum is to scaffold the learning experiences and to relate tacit knowledge with formal
knowledge. This would involve trans-disciplinary linkages that would form the core of the learning process. Perspectives,
SEWA (Social Empowerment through Work and Action), Life Skills and Research would be the constituents of this 'Core'.
The Core skills are the most significant aspects of a learner's holistic growth and learning curve.
The International Curriculum has been designed keeping in view the foundations of the National Curricular Framework
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millions of learners, many of whom are now global citizens.
The Board does not interpret this development as an alternative to other curricula existing at the international level, but as
an exercise in providing the much needed Indian leadership for global education at the school level. The International
Curriculum would evolve on its own, building on learning experiences inside the classroom over a period of time. The
Board while addressing the issues of empowerment with the help of the schools' administering this system strongly
recommends that practicing teachers become skillful learners on their own and also transfer their learning experiences to
their peers through the interactive platforms provided by the Board.
I profusely thank Shri G. Balasubramanian, former Director (Academics), CBSE, Ms. Abha Adams and her team and Dr.
Sadhana Parashar, Head (Innovations and Research) CBSE along with other Education Officers involved in the
development and implementation of this material.
The CBSE-i website has already started enabling all stakeholders to participate in this initiative through the discussion
forums provided on the portal. Any further suggestions are welcome.
Vineet Joshi
Chairman
Advisory Conceptual Framework
Shri Vineet Joshi, Chairman, CBSE Shri G. Balasubramanian, Former Director (Acad), CBSE
Shri Shashi Bhushan, Director(Academic), CBSE Ms. Abha Adams, Consultant, Step-by-Step School, Noida
Dr. Sadhana Parashar, Head (I & R),CBSE
Ideators
Ms. Aditi Misra Ms. Anuradha Sen Ms. Jaishree Srivastava Dr. Rajesh Hassija
Ms. Amita Mishra Ms. Archana Sagar Dr. Kamla Menon Ms. Rupa Chakravarty
Ms. Anita Sharma Ms. Geeta Varshney Dr. Meena Dhami Ms. Sarita Manuja
Ms. Anita Makkar Ms. Guneet Ohri Ms. Neelima Sharma Ms. Himani Asija
Dr. Anju Srivastava Dr. Indu Khetrapal Dr. N. K. Sehgal Dr. Uma Chaudhry
Material Production Groups: Classes IX-X
English : Mathematics : Science : History :
Ms. Sarita Manuja Dr. K.P. Chinda Ms. Charu Maini Ms. Jayshree Srivastava
Ms. Renu Anand Dr. Ram Avtar Gupta
Ms. S. Anjum Ms. M. Bose
Ms. Gayatri Khanna Dr. Mahender Shankar
Ms. Meenambika Menon Ms. A. Venkatachalam
Ms. P. Rajeshwary Mr. J.C. Nijhawan
Ms. Novita Chopra Ms. Smita Bhattacharya
Ms. Neha Sharma Ms. Reemu Verma
Ms. Neeta Rastogi
Ms. Sarabjit Kaur Ms. Himani Asija
Ms. Pooja Sareen
Ms. Ruchika Sachdev
Geography: P o l i t i c a l S c i e n c e :
Economics:
Ms. Deepa Kapoor M s . S h a r m i l a B a k s h i
Ms. Mridula Pant
Ms. Bharti Dave M s . A r c h a n a S o n i
Ms. Bhagirathi Ms. Srilekha Mr. Pankaj Bhanwani
Ms. Archana Sagar Ms. Ambica Gulati
Ms. Manjari Rattan
Material Production Groups: Classes VI-VIII
English : Science : Mathematics : Geography:
Ms. Rachna Pandit Dr. Meena Dhami Ms. Seema Rawat Ms. Suparna Sharma
Ms. Neha Sharma Mr. Saroj Kumar Ms. N. Vidya Ms. Leela Grewal
Ms. Sonia Jain Ms. Rashmi Ramsinghaney Ms. Mamta Goyal History :
Ms. Dipinder Kaur Ms. Seema kapoor Ms. Chhavi Raheja Ms. Leeza Dutta
Ms. Sarita Ahuja Ms. Priyanka Sen Political Science: Ms. Kalpana Pant
Dr. Kavita Khanna Ms. Kanu Chopra
Ms. Keya Gupta Ms. Shilpi Anand
Material Production Group: Classes I-V
Dr. Indu Khetarpal Ms. Rupa Chakravarty Ms. Anita Makkar Ms. Nandita Mathur
Ms. Vandana Kumar Ms. Anuradha Mathur Ms. Kalpana Mattoo Ms. Seema Chowdhary
Ms. Anju Chauhan Ms. Savinder Kaur Rooprai Ms. Monika Thakur Ms. Ruba Chakarvarty
Ms. Deepti Verma Ms. Seema Choudhary Mr. Bijo Thomas Ms. Mahua Bhattacharya
Ms. Ritu Batra Ms. Kalyani Voleti
Coordinators:
Dr. Sadhana Parashar, Ms. Sugandh Sharma, Dr. Srijata Das, Dr. Rashmi Sethi,
Head (I and R) E O (Com) E O (Maths) O (Science)
Shri R. P. Sharma, Consultant Ms. Ritu Narang, RO (Innovation) Ms. Sindhu Saxena, R O (Tech) Shri Al Hilal Ahmed, AEO
Ms. Seema Lakra, S O Ms. Preeti Hans, Proof Reader
1. Syllabus 1
2. Scope document 2
3. Teacher's Support Material 3
vTeacher Note 4
vActivity Skill Matrix 7
vWarm Up W1 8
Planting trees at given points
vWarm Up W2 8
Speak aloud
vPre -Content P1 9
Making shapes by joining points
vPre -Content P2 9
Recalling Pythagoras theorem
vContent Worksheet CW1 10
Distance formula
vContent Worksheet CW2 10
Application of distance formula
vContent Worksheet CW3 11
Section formula
vContent Worksheet CW4 11
Application of Section formula
vContent Worksheet CW5 12
Transformations
vPost Content Worksheet PCW1 13
vPost Content Worksheet PCW2 13
v Post Content Worksheet PCW3 13
vPost Content Worksheet PCW4 13
vPost Content Worksheet PCW5 13
vAssessment Plan
4. Study Material 14
5. Student's Support Material 40
vSW1: Warm Up (W1) 40
Planting trees at given points
vSW2: Warm Up (W2) 43
Speak aloud
vSW3: Pre Content (P1) 44
Making shapes by joining points
vSW4: Pre Content (P2) 48
Recalling Pythagoras theorem
vSW5: Content (CW1) 50
Distance formula
vSW6: Content (CW2) 52
Application of distance formula
vSW7: Content (CW3) 62
Section formula
vSW8: Content (CW4) 64
Application of section formula
vSW9: Content (CW5) 67
Transformations
vSW10 : Post Content (PCW1) 77
vSW11 : Post Content (PCW2) 78
vSW 12 : Post Content (PCW3) 80
vSW 13 : Post Content (PCW4) 80
vSW 14 : Post Content (PCW5) 81
6. Suggested Videos & Extra Readings. Videos & Extra Readings. 82
SYLLABUS
Class – X, Unit – 6 (Core)
Revisit Location of a point in plane as (x, y), representation of line as
coordinate y= m x + c, where m is gradient and c is y- intercept.
geometry
Distance Distance of a point P(x, y) from origin(0,0) as
between two OP=
points in a
P(x, y)
coordinate plane
O(0,0)
Distance formula to find distance between points A ( ) and
B( )as
AB = +( - )2
Section formula point of internal division
Transformations Translation as transformation that slides figure, translation of a
point from P(x, y)to Q(x+a, y+a),
Translation of a line,
Reflection as transformation that flips everything over, reflection
across x-axis, reflection across y- axis, reflection across the line
x=constant, reflection across the line y = constant
1
SCOPE DOCUMENT
Key concepts/terms:
Distance formula
Section formula
Translation
Reflection
Learning Objectives: -The students will be able to
Locate a point (x, y) in Cartesian plane.
Determine whether the given point lies on the line y = mx + c
Draw the line y = mx + c in Cartesian plane by determining the points on the line
can tell the gradient / slope of given line, its x or y intercept, its point of intersection
with x – axis or y – axis.
Can find the distance between two points in a cartesian plane using distance
formula.
Determine the point of internal division of line.
Describe transformation of a figure on plane as movement of a figure in place when
all points lie on figure change their coordinates in the same manner.
Understand translation as transformation that slides figure in let or right, up or
down and can also write it with proper notation.
Understand reflection across x-axis or y-axis line x=const. and y = const and can also
write point of reflection across axis of symmetry in right notation.
Cross-Curricular Link :
1. A coordinate system is setup to that (o, o) is the cantre of the sun (67,499,999,
67,512,000) the centre of the earth and (67,600,000, 62,728,916) the centre of the
moon, If all distance are in miles, find the distance from the centre of earth and
the distance from the center of the earth to the center of the moon.
2. During a total solar eclipse, the centre of the sun, moon and with earth are
collinear and the moon is located between the sun and the earth. Using the
distances from above statement, give the coordinate of the centers of the moon
and earth during a total solar eclipse if the sun is placed at the origin and the
moon and earth are placed on the positive x-axis,
2
