{"id":2725,"date":"2020-12-22T10:19:42","date_gmt":"2020-12-22T04:49:42","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=2725"},"modified":"2020-12-22T12:06:48","modified_gmt":"2020-12-22T06:36:48","slug":"cartesian-coordinate-system","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/cartesian-coordinate-system\/","title":{"rendered":"What Is The Cartesian Coordinate System"},"content":{"rendered":"

What Is The Cartesian Coordinate System<\/strong><\/h2>\n

In Cartesian co-ordinates<\/a> 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.
\n\"WhatDraw 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.<\/p>\n

    \n
  1. Axes of Co-ordinates<\/strong>
    \nIn the figure OX and OY are called as x-axis and y-axis respectively and both together are known as axes of co-ordinates.<\/li>\n
  2. Origin<\/strong>
    \nIt is point O of intersection of the axes of co-ordinates.<\/li>\n
  3. Co-ordinates of the Origin<\/strong>
    \nIt has zero distance from both the axes so that its abscissa and ordinate are both zero. Therefore, the coordinates of origin are (0, 0).<\/li>\n
  4. Abscissa<\/strong>
    \nThe distance of the point P from y-axis is called its abscissa. In the figure OM = PN is the Abscissa.<\/li>\n
  5. Ordinate<\/strong>
    \nThe distance of the point P from x-axis is called its ordinate. ON = PM is the ordinate in the figure.<\/li>\n
  6. Quadrant<\/strong>
    \nThe 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.
    \nA quadrant is 1\/4 part of a plane divided by co-ordinate axes.
    \n\"What
    \n(i) XOY is called the first quadrant
    \n(ii) YOX’ the second.
    \n(iii) X’OY’ the third.
    \n(iv) Y’OX the fourth
    \nas marked in the figure.<\/li>\n<\/ol>\n

    RULES OF SIGNS OF CO-ORDINATES<\/strong><\/p>\n

      \n
    1. In the first quadrant, both co-ordiantes i.e., abscissa and ordinate of a point are positive.<\/li>\n
    2. In the second quadrant, for a point, abscissa is negative and ordinate is positive.<\/li>\n
    3. In the third quadrant, for a point, both abscissa and ordinate are negative.<\/li>\n
    4. In the fourth quadrant, for a point, the abscissa is positive and the ordinate is negative.\"What<\/li>\n<\/ol>\n

       <\/p>\n

      Cartesian Coordinate System Example Problems With Solutions<\/strong><\/h2>\n

      Example 1: \u00a0 \u00a0<\/strong>From the adjoining figure find
      \n\"What
      \n(i) Abscissa
      \n(ii) Ordinate
      \n(iii) Co-ordinates of a point P
      \nSolution: \u00a0 \u00a0<\/strong>(i) Abscissa = PN = OM = 3 units
      \n(ii) Ordinate = PM = ON = 4 units
      \n(iii) Co-ordinates of the point P = (Abscissa, ordinate) = (3, 4)<\/p>\n

      Example 2: \u00a0 \u00a0<\/strong>Determine
      \n\"What
      \n(i) Abscissa (ii) ordinate (iii) Co-ordinates of point P given in the following figure.
      \nSolution: \u00a0 \u00a0<\/strong>(i) Abscissa of the point P = \u2013 NP = \u2013OM = \u2013 a
      \n(ii) Ordinate of the point P = MP = ON = b
      \n(iii) Co-ordinates of point P = (abscissa, ordinate)
      \n= (\u2013a, b)<\/p>\n

      Example 3: \u00a0 \u00a0<\/strong>Write down the (i) abscissa (ii) ordinate (iii) Co-ordinates of P, Q, R and S as given in the figure.
      \n\"What
      \nSolution: \u00a0 \u00a0Point P<\/strong>
      \nAbscissa of P = 2; Ordinate of P = 3
      \nCo-ordinates of P = (2, 3)
      \nPoint Q<\/strong>
      \nAbscissa of Q = \u2013 2; Ordinate of Q = 4
      \nCo-ordinate of Q = (\u20132, 4)
      \nPoint R<\/strong>
      \nAbscissa of R = \u2013 5; Ordinate of R = \u2013 3
      \nCo-ordinates of R = (\u20135, \u20133)
      \nPoint S<\/strong>
      \nAbscissa of S = 5; Ordinate of S = \u2013 1
      \nCo-ordinates of S = (5, \u2013 1)<\/p>\n

      Example 4: \u00a0 \u00a0<\/strong>Draw a triangle ABC where vertices A, B and C are (0, 2), (2, \u2013 2), and (\u20132, 2) respectively.
      \nSolution: \u00a0 \u00a0<\/strong>Plot the point A by taking its abscissa O and ordinate = 2.
      \nSimilarly, plot points B and C taking abscissa 2 and \u20132 and ordinates \u2013 2 and 2 respectively. Join A, B and C. This is the required triangle.
      \n\"What<\/p>\n

      Example 5: \u00a0 \u00a0<\/strong>Draw a rectangle PQRS in which vertices P, Q, R and S are (1, 4), (\u20135, 4), (\u20135, \u20133) and
      \n(1, \u2013 3) respectively.
      \nSolution: \u00a0 \u00a0<\/strong>Plot the point P by taking its abscissa 1 and ordinate \u2013 4.
      \nSimilarly, plot the points Q, R and S taking abscissa as \u20135, \u20135 and 1 and ordinates as 4, \u2013 3 and \u20133 respectively.
      \nJoin the points PQR and S. PQRS is the required rectangle.
      \n\"What<\/p>\n

      Example 6: \u00a0 \u00a0<\/strong>Draw a trapezium ABCD in which vertices A, B, C and D are (4, 6), (\u20132, 3), (\u20132, \u20135) and
      \n(4, \u20137) respectively.
      \nSolution: \u00a0 \u00a0<\/strong>Plot the point A taking its abscissa as 4 and ordinate as 6.
      \nSimilarly plot the point B, C and D taking abscissa as \u2013 2, \u20132 and 4 and ordinates as 3, \u2013 5, and \u20137 respectively. Join A, B, C and D ABCD is the required trapezium.
      \n\"What<\/p>\n

       <\/p>\n","protected":false},"excerpt":{"rendered":"

      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. […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[5],"tags":[1167,1166,1170,1171,1165,1168,1169],"yoast_head":"\nWhat Is The Cartesian Coordinate System - A Plus Topper<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.aplustopper.com\/cartesian-coordinate-system\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What Is The Cartesian Coordinate System\" \/>\n<meta property=\"og:description\" content=\"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. 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