Basic Maths Section [C] Co-Ordinate Geometry

University:
Santa Ana College
Course:
MATH 170 | Pre-Calculus Mathematics
Academic year:

2023
Views:

88

Pages:

2
Author:

cravelingstnw

SECTION [C] : CO-ORDINATE GEOMETRY To specify the position of a point in space, we use right handed rectangular axes coordinate system. This system consists of (i) origin (ii) axis or axes. If point is known to be on a given line or in a particular direction, only one coordinate is necessary to specify its position, if it is in a plane, two coordinates are required, if it is in space three coordinates are needed. ORIGIN This is any fixed point which is convenient to you. All measurement are taken w.r.t. this fixed point. Axis or Axes Any fixed direction passing through origin and convenient to you can be taken as an axis. If the position of a point or position of all the points under consideration always happen to be in a particular direction, then only one axis is required. This is generally called the x-axis. If the positions of all the points under consideration are always in a plane, two perpendicular axes are required. These are generally called x and y-axis. If the points are distributed in a space, three perpendicular axes are taken which are called x, y and z-axis. Position of a point in xy plane The position of a point is specified by its distances from origin along (or parallel to) x and y-axis as shown in figure. y x (x,y) y origin (0,0) x x Here x-coordinate and y-coordinate is called abscissa and ordinate respectively. Distance Formula The distance between two points (x1, y1) and (x2, y2) is given by d  x  x1    y2  y1  2 2 Ex. Sol. For point (2, 14) find abscissa and ordinates. Also find distance from y and x-axis. Abscissa = x-coordinate = 2 = distance from y-axis. Ordinate = y-coordinate = 14 = distance from x-axis. Ex. Find value of a if distance between the points (–9 cm, a cm) and (3 cm, 3cm) is 13 cm. Sol. By using distance formula d   132 = 122 + (3–a)2 Ex. Sol.  x2  x1    y2  y1  2  (3–a)2 = 132 – 122 = 52 2 2  13  13   9   3  a   (3–a) = ±5  a = –2 cm or 8 cm 2 2 A dog wants to catch a cat. The dog follows the path whose equation is y–x = 0 while the cat follows the path whose equation is x2 + y2 = 8. The coordinates of possible points of catching the cat are : (A) (2, –2) (B) (2, 2) (C) (–2, 2) (D) (–2, –2) (BD) BASIC MATHS & VECTOR Let catching point be (x1, y1) then, y1–x1=0 and x12 + y12 = 8 Therefore, 2x12 = 8  x12 =4  x1=±2; So possible points are (2, 2) and (–2, –2). Slope of a Line The slope of a line joining two points A(x1, y1) and B(x2, y2) is denoted by m and is given by m y y2  y1   tan  [If both axes have identical scales x x2  x1 Here  is the angle made by line with positive x-axis. Slope of a line is a quantitative measure of inclination. Ex. Sol. Distance between two points ( 8, – 4) and (0, a) is 10. All the values are in the same unit of length. Find the positive value of a. (2) From distance formula (8–0)2 + (–4–a)2 = 100 (4+a)2 = 36 a =2

Basic Maths Section [C] Co-Ordinate Geometry

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