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 CBSE Maths eBooks CBSE Guess > eBooks > Class X > Maths Part II by Mr. M. P. Keshari Chapter 17: Co-ordinate Geometry
We are already familiar with plotting a point on a plane graph paper. For this we take two perpendicular lines XoX’ and YoY’ intersecting at O. XOX’ is called x-axis or abscissa and YoY’ is called y-axis or ordinate. Point in a plane Let us take a point P in a plane. Let XOX’ and YOY’ be pendicualr to each other at O. are drawn. If OM = x and ON = y then x-coordinate of P is x and y-coordinate of P is y. Here we write x-coordinate first. Hence (x, y) and (y, x) are different point whenever . The two lines XOX’ and YOY’ divides the plane into four parts called quadrants. XOY, YOX’, X’OY’ and Y’OX are respectively the first second, third and and fourth quadrants. We take the direction from O to X and O to Y as positive and the direction from O to X’ and O to Y’ as negative. Distance between two points Let P (x1, y1) and Q (x2, y2) be the two points. We have to find PQ. OM = x1, PM = y1 = RN ON = x2, QN = y2 PR = MN = ON – OM = x2 – x1 QR = QN – RN = y2 – y1 By Pythagoras theorem PQ2 = PR2 + QR2 = (x2 - x1)2 + (y2 – y1)2 If x1 = 0, y1 = 0, x2 = x and y2 = y Then Section Formula Let P (x, y) divided a line AB such that AP : PB = m1 : m2. Let coordinates of A are (x1, y1) and B are (x2, y2). It is obvious that Taking, Similarity Note (i) if P is mid point of AB, then AP : PB = 1 : 1 (ii) If m1 : m2 = k, then coordinates of P are   Maths by Mr. M. P. Keshari