• Skip to main content
  • Skip to secondary menu
  • Skip to primary sidebar
  • Skip to footer
  • ICSE Solutions
    • ICSE Solutions for Class 10
    • ICSE Solutions for Class 9
    • ICSE Solutions for Class 8
    • ICSE Solutions for Class 7
    • ICSE Solutions for Class 6
  • Selina Solutions
  • ML Aggarwal Solutions
  • ISC & ICSE Papers
    • ICSE Previous Year Question Papers Class 10
    • ISC Previous Year Question Papers
    • ICSE Specimen Paper 2021-2022 Class 10 Solved
    • ICSE Specimen Papers 2020 for Class 9
    • ISC Specimen Papers 2020 for Class 12
    • ISC Specimen Papers 2020 for Class 11
    • ICSE Time Table 2020 Class 10
    • ISC Time Table 2020 Class 12
  • Maths
    • Merit Batch

A Plus Topper

Improve your Grades

  • CBSE Sample Papers
  • HSSLive
    • HSSLive Plus Two
    • HSSLive Plus One
    • Kerala SSLC
  • Exams
  • NCERT Solutions for Class 10 Maths
  • NIOS
  • Chemistry
  • Physics
  • ICSE Books

What Is The Cartesian Coordinate System

December 22, 2020 by Veerendra

What Is The Cartesian Coordinate System

In Cartesian co-ordinates the position of a point P is determined by knowing the distances from two perpendicular lines passing through the fixed point. Let O be the fixed point called the origin and XOX’ and YOY’, the two perpendicular lines through O, called Cartesian or Rectangular co-ordinates axes.
What Is The Cartesian Coordinate System 1Draw PM and PN perpendiculars on OX and OY respectively. OM (or NP) and ON (or MP) are called the x-coordinate (or abscissa) and y-coordinate (or ordinate) of the point P respectively.

  1. Axes of Co-ordinates
    In the figure OX and OY are called as x-axis and y-axis respectively and both together are known as axes of co-ordinates.
  2. Origin
    It is point O of intersection of the axes of co-ordinates.
  3. Co-ordinates of the Origin
    It has zero distance from both the axes so that its abscissa and ordinate are both zero. Therefore, the coordinates of origin are (0, 0).
  4. Abscissa
    The distance of the point P from y-axis is called its abscissa. In the figure OM = PN is the Abscissa.
  5. Ordinate
    The distance of the point P from x-axis is called its ordinate. ON = PM is the ordinate in the figure.
  6. Quadrant
    The axes divide the plane into four parts. These four parts are called quadrants. So, the plane consists of axes and quadrants. The plane is called the cartesian plane or the coordinate plane or the xy-plane. These axes are called the co-ordinate axes.
    A quadrant is 1/4 part of a plane divided by co-ordinate axes.
    What Is The Cartesian Coordinate System 2
    (i) XOY is called the first quadrant
    (ii) YOX’ the second.
    (iii) X’OY’ the third.
    (iv) Y’OX the fourth
    as marked in the figure.

RULES OF SIGNS OF CO-ORDINATES

  1. In the first quadrant, both co-ordiantes i.e., abscissa and ordinate of a point are positive.
  2. In the second quadrant, for a point, abscissa is negative and ordinate is positive.
  3. In the third quadrant, for a point, both abscissa and ordinate are negative.
  4. In the fourth quadrant, for a point, the abscissa is positive and the ordinate is negative.What Is The Cartesian Coordinate System 3

 

Cartesian Coordinate System Example Problems With Solutions

Example 1:    From the adjoining figure find
What Is The Cartesian Coordinate System 4
(i) Abscissa
(ii) Ordinate
(iii) Co-ordinates of a point P
Solution:    (i) Abscissa = PN = OM = 3 units
(ii) Ordinate = PM = ON = 4 units
(iii) Co-ordinates of the point P = (Abscissa, ordinate) = (3, 4)

Example 2:    Determine
What Is The Cartesian Coordinate System 5
(i) Abscissa (ii) ordinate (iii) Co-ordinates of point P given in the following figure.
Solution:    (i) Abscissa of the point P = – NP = –OM = – a
(ii) Ordinate of the point P = MP = ON = b
(iii) Co-ordinates of point P = (abscissa, ordinate)
= (–a, b)

Example 3:    Write down the (i) abscissa (ii) ordinate (iii) Co-ordinates of P, Q, R and S as given in the figure.
What Is The Cartesian Coordinate System 6
Solution:    Point P
Abscissa of P = 2; Ordinate of P = 3
Co-ordinates of P = (2, 3)
Point Q
Abscissa of Q = – 2; Ordinate of Q = 4
Co-ordinate of Q = (–2, 4)
Point R
Abscissa of R = – 5; Ordinate of R = – 3
Co-ordinates of R = (–5, –3)
Point S
Abscissa of S = 5; Ordinate of S = – 1
Co-ordinates of S = (5, – 1)

Example 4:    Draw a triangle ABC where vertices A, B and C are (0, 2), (2, – 2), and (–2, 2) respectively.
Solution:    Plot the point A by taking its abscissa O and ordinate = 2.
Similarly, plot points B and C taking abscissa 2 and –2 and ordinates – 2 and 2 respectively. Join A, B and C. This is the required triangle.
What Is The Cartesian Coordinate System 7

Example 5:    Draw a rectangle PQRS in which vertices P, Q, R and S are (1, 4), (–5, 4), (–5, –3) and
(1, – 3) respectively.
Solution:    Plot the point P by taking its abscissa 1 and ordinate – 4.
Similarly, plot the points Q, R and S taking abscissa as –5, –5 and 1 and ordinates as 4, – 3 and –3 respectively.
Join the points PQR and S. PQRS is the required rectangle.
What Is The Cartesian Coordinate System 8

Example 6:    Draw a trapezium ABCD in which vertices A, B, C and D are (4, 6), (–2, 3), (–2, –5) and
(4, –7) respectively.
Solution:    Plot the point A taking its abscissa as 4 and ordinate as 6.
Similarly plot the point B, C and D taking abscissa as – 2, –2 and 4 and ordinates as 3, – 5, and –7 respectively. Join A, B, C and D ABCD is the required trapezium.
What Is The Cartesian Coordinate System 9

 

Filed Under: Mathematics Tagged With: Cartesian co-ordinates, Cartesian Coordinate System, Cartesian Coordinates Example Problems, Cartesian Coordinates Examples, Co-Ordinate Geometry, Rectangular Co-ordinates, Rules of Signs of Co-ordinates

Primary Sidebar

  • MCQ Questions
  • RS Aggarwal Solutions
  • RS Aggarwal Solutions Class 10
  • RS Aggarwal Solutions Class 9
  • RS Aggarwal Solutions Class 8
  • RS Aggarwal Solutions Class 7
  • RS Aggarwal Solutions Class 6
  • ICSE Solutions
  • Selina ICSE Solutions
  • Concise Mathematics Class 10 ICSE Solutions
  • Concise Physics Class 10 ICSE Solutions
  • Concise Chemistry Class 10 ICSE Solutions
  • Concise Biology Class 10 ICSE Solutions
  • Concise Mathematics Class 9 ICSE Solutions
  • Concise Physics Class 9 ICSE Solutions
  • Concise Chemistry Class 9 ICSE Solutions
  • Concise Biology Class 9 ICSE Solutions
  • ML Aggarwal Solutions
  • ML Aggarwal Class 10 Solutions
  • ML Aggarwal Class 9 Solutions
  • ML Aggarwal Class 8 Solutions
  • ML Aggarwal Class 7 Solutions
  • ML Aggarwal Class 6 Solutions
  • HSSLive Plus One
  • HSSLive Plus Two
  • Kerala SSLC

Recent Posts

  • Air Pollution Essay for Students and Kids in English
  • 10 Lines on Satya Nadella for Students and Children in English
  • Essay on Wonders of Science | Wonders of Science for Students and Children in English
  • My Childhood Memories Essay | Essay on My Childhood Memories for Students and Children in English
  • Essay On Sports And Games | Sports And Games Essay for Students and Children in English
  • Clean India Slogans | Unique and Catchy Clean India Slogans in English
  • Animals that Start with Z | Listed with Pictures, List of Animals Starting with Z & Interesting Facts
  • Positive Words That Start With S | List of Positive Words Starting With S Meaning, Examples,Pictures and Facts
  • Positive Words that Start with B | List of 60 Positive Words Starting with B Pictures and Facts
  • Humanity Essay | Essay on Humanity for Students and Children in English
  • Teenage Pregnancy Essay | Essay on Teenage Pregnancy for Students and Children in English

Footer

  • RS Aggarwal Solutions
  • RS Aggarwal Solutions Class 10
  • RS Aggarwal Solutions Class 9
  • RS Aggarwal Solutions Class 8
  • RS Aggarwal Solutions Class 7
  • RS Aggarwal Solutions Class 6
  • Picture Dictionary
  • English Speech
  • ICSE Solutions
  • Selina ICSE Solutions
  • ML Aggarwal Solutions
  • HSSLive Plus One
  • HSSLive Plus Two
  • Kerala SSLC
  • Distance Education
DisclaimerPrivacy Policy
Area Volume Calculator