Page 1 : Chapter 12, Co-Ordinate Geometry, , I Co-ordinates:, , Let XOX' and YOY' be two pe i ines i i, , tpendicular lines intersecting atO., These two lines are called axes. XOX" is called the X-axis YOY’ is, , called the Y-axis and O is called the origin. These axes help us to locate, any point P., , AY, , , , ‘, , , , , , , , , , vY', , Fig 1.1. :, , Let P be any point on the plane XOY. Draw PL and PM, perpendicular to X and Y axes. The length PM = x is called the x coordinate of the point P and the length PL = y is called the y co-ordinate, of P. PM and PL are called the co-ordinates of P. This ordered pair is, denoted by (x,y). Note that OL = MP = x and OM = PL = y. The x coordinates of the point P is also calied the abscissa and the y co-ordinate, of P is called the ordinate; the co-ordinates of the origin O are (0,0), , OX is called the positive direction of X-axis and OX’ is called the, negative direction of the X-axis. OY is called the positive direction of, the Y-axis and OY' is called the negative direction of the Y-axis. The, lines XOX' and YOY' divide the plane into four quadrants. The four, quadrants are represented in the following figure.

Page 2 : Business Mathematic,, 316, , , , AY, Il !, nd, ———— FJ 4, x' a, m IV, y', Fig. 1.2, The sign of co-ordinates in the four quadrants is given below:, Quadrant Co-ordinate, x : y, ! a, Ml - i, Vv + , For example, the points (2,3), (-3, ,th 3), (-3, 4), (-1, -1) and (5,-2) are, represented by the points.A,B,C.D respectively in the auowine Fe

Page 3 : Co-ordinate Geometry, , 317, , , , A, (-3,4) (2,3), B, <<, es 5 (5, -2), , , , Fig.13, , The method of representing a point by means of co-ordinates was, introduced by the French Mathematician. Rene Descartes.

Page 5 : Co-ordinate Geometry, 319, , JExa ple 1:, Find the distance betw, i, ¥ Solution: en the points (4,7) and (2,5)., , Pp ., Let P and Q be the points (4,7) and (-2,5) respectively,, , PQ? = (r1-x9)2 419592, = (442)? + (7-5)2 = “ted =49, - PQ= V40 units,, , Example 2:, - ‘, , come mts (4:3). (7-1) and (9,3) are the vertices of an, , Solution: (C.A.Nov.1976), Let A,B,C be the points (4,3), (7, -1, Then AB? = (4-7)? + (341)? = 9416 = 25, BC = (7-924 (-1 3)? = 44 16= 20, AC? = (4-9)243-32 = 95, , “.AB=5, BC=J20, aces,, , Since the sum of two Sides is greater than the third, the points, , fi i : :, — Also AB = BC = 5. -. The triangle is an isosceles, , ) and (9,3) respecuvely., , Example 3:, Show that the points (6,6), (2,3) and (4,7) are the vertices of a ri, gael wang. ou (C.A.May ae, olufion: ., Let A,B,C be the points (6,6), (2,3) and (4,7) respectively., ABZ = (6 - 2)2 + (6 - 3)? = 1649 = 25, BC? = (2 - 4)2 + (3-7)2 = 4416 = 20, AC2 = (6 -4)2 + 6-7)2 = 441 =5, AC2 + BC? = 2045 =25 = AB2, .. The points are the vertices of a right angled triangle., , Example 4:, , Show that the points (7,9), (3, -7) and (-3, 3) are the vertices of a, right angled isosceles triangle. (C.A.Nov.1977), Solution: ‘, , Let A,B,C be the points (7,9), (3,-7), (-3,3) respectively., , AB2 = (7 -3)2 + 9 +7)? = 16+256 = 272, , BC2 = (343)2 + (-7 -3)2 = 364100 = 136, , AC2 = (743)2 + (9 - 3) = 100 +36 + 136, , BC2 + AC2 = 136 + 136 = 272 = AB2