Coordinate Geometry

Category: Education

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The branch of mathematics which deals with location of objects in 2-D (dimensional) plane is called coordinate geometry. Need to present your work in most impressive & informative manner i.e. through Power Point Presentation call us at skype Id: kumar_sukh79 or mail us: for using my service.


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Coordinate Geometry Y-axis X-axis

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Let’s refresh our knowledge… LATITUDE Parallel lines which appears horizontal, running from East to West direction EAST NOR TH SOUTH LONGITUDE Parallel lines which appears vertical, running from North pole to South pole WEST

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The branch of mathematics which deals with location of objects in 2-D (dimensional) plane is called coordinate geometry. coordinate geometry

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As we have just refreshed our knowledge about geographical terms latitude and longitude. This concept geography is used in our daily lives. Lets go through one activity:- Consider a glass is kept on the table, you want to define the position of that glass. As we can see in the figure 3.1, the glass is near two edges of a table i.e. left and bottom edge. Now we can decide the position of the glass as shown in figure 3.2. Fig. 3.1 Fig. 3.2 C ARTESIAN SYSTEM… TABLE GLASS TABLE GLASS

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Fig. 3.2 Edge-1 Edge-2 As we have seen in our example, the position is defined by two edges. These edges are mutually perpendicular to each other. These edges are known as axes . Thus, the system used for describing the position of an object in a plane is called as CARTESIAN SYSTEM C ARTESIAN SYSTEM… TABLE GLASS

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ACTIVITY: Draw a plan of the seating in your classroom, pushing the desks together. Represent each desk by a square, in it write the name of the student occupying the desk, position of each student is represented as:- a) The row in which he/she sits, b) The column in which he/she sits ANSWER

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A 4 3 2 1 0 4 3 2 1 COLUMN ROW Write the name e.g.:- ‘A’ is sitting on desk lying in 2 nd row and 4 th column ( 4,2) This activity gives you a brief idea of Cartesian System. DESK Name of the student occupying the desk

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C OORDINATE AXES… ORIGIN is the Point of Intersection ‘O ’ y 1 x 1 Plotting a point in the plane if its Coordinates are given… Two fixed mutually perpendicular lines which determine the position of a point in a plane are called COORDINATE AXES

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Type of Axes X-axis :- The horizontal axis is called X -axis. X- point/coordinate is called “abscissa ”. Y-axis : The vertical axis is called Y -axis. Y- coordinate/point is called “ordinate ”.

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S OME ILLUSTRATIONS… Q.1. On which axis do the given points lie? i ) (4,0) ii) (0,-5) iii) (0,9) iv) (-7,0) v) (6,0) vi) (0,8) Ans. i ) x-axis iv) x-axis ii) y-axis v) x-axis iii) y-axis vi) y-axis

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0 X 1 X Y 1 Y -1 -2 -3 -4 -5 -6 1 2 3 4 5 6 6 5 4 3 2 1 -6 -5 -4 -3 -2 -1     3.) (0,6) 2.) (0,3) 4.) (0,-2) 1.) (-5,0) Q.2. Write the coordinates of a point:- 1) Lying on x-axis to the left of origin at a distance of 5 units 2) Lying on y-axis to the upper part of origin at distance of 3 units 3) Above x-axis, lying on y-axis at distance of 6 units 4) Below x-axis, lying on y-axis at a distance of 2 units ANSWER

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Quadrant 2 X X 1 Y 1 Y Quadrant 1 Quadrant 4 Quadrant 3 Both these axes i.e. X-axis & Y-axis divide the plane into four parts known as QUADRANTS. **Note: The coordinates of origin:- (0,0) Q UADRANTS…

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QUADRANTS ABSCISSA ORDINATE QUADRANT 1 + ve (Positive) + ve (Positive) QUADRANT 2 - ve (Negative) + ve (Positive) QUADRANT 3 - ve (Negative) - ve (Negative) QUADRANT 4 + ve (Positive) - ve (Negative) Sign Convention for Quadrants

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(Abscissa, Ordinate) Convention Defining point A Position Let’s define the position of a point ‘A’ in the plane… Point A (2,1) ABSCISSA ORDINATE A(2,1) 2 1 1 2 

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Point A is written as (2,1 ) where 2 is Abscissa & 1 is Ordinate. ** Note (1,2) is not equal to (2,1 ). A(2,1) 2 1 1 2  o

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(0,4) S OME ILLUSTRATIONS… Q.1. In which quadrant do the following points lie? i ) (-3, 2) ii) (4, 6) iii) (5, -1) iv) (0, 4)

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Answers i ) As abscissa is negative and ordinate is positive so (-3, 2) lies in Quadrant 2 ii) As abscissa and ordinate both are positive, so (4, 6) lies in Quadrant 1 iii) As abscissa is positive and ordinate is negative so (5, -1) lies in Quadrant 4 iv) As abscissa is “zero”, then this point lies on y – axis itself. As ordinate is positive (0, 4) lies on upper y – axis .

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Points to Remember while plotting a point on a plane… There are few steps that we should always follow to plot a point on a plane, these are as follows: Draw two mutually perpendicular lines on a graph paper (or we can own make on any paper) one horizontal and other vertical. Mark their intersection point as O (origin). The horizontal line as XOX 1 ( X – axis), vertical line as YOY 1 , (Y – axis). Choose suitable points according to the question. The points should be in some pattern (normal 1, 2, 3, 4 _ _ _ OR 2, 4, 6, 8 _ _ _ OR 3, 6, 9 _ _ _ OR 10, 20, 30, _ _ _). To plot point P(a, b) start from origin (‘O’) and move ‘a’ units along x – axis (right side if ‘x’ is a positive number and left side if ‘x’ is a negative number). Suppose we arrive at point ‘S’, then move ‘b’ units vertically upward (if ordinate is a positive number) or downward (if ordinate is a negative number). The point where we arrive is our final destination P(a, b) . 1 2 3 4

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Time allowed: 10 minutes HOTS (Higher Order Thinking Skills) 1) The perpendicular distance of a point P(4,3) from y- axis is:- a) 4 b) 3 c) 5 d) 7 Answer (a) 2) The perpendicular distance of a point P(8,2) from x-axis is:- a) 2 b) 3 c) 4 d) 6 Answer (a) 3) The area of triangle formed by the points A(2,0), B(6,0), C(1,6) is Height Base a)24 sq. units c) 10 sq. units b)12 sq. units d)none of these Answer (b) [Hint: Area of triangle = ½ × base × height] 4) The measure of angle between the coordinate axes is:- a) 0 0 b) 90 0 c) 180 0 d) 360 0 Answer (b) 5) Points (-4,0) and (6,0) lie a) in first Quadrant c) y-axis b) x-axis d) second Quadrant Answer (b)

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6)Two points having same ordinates but different abscissa lie on a) x-axis c) a line parallel to y-axis b) y-axis d) a line parallel to x-axis Answer (d)   7)The x – coordinate of every point on y-axis is ________ a) Variable b) Constant c) Zero d) None of these Answer (c) 8)In order to locate the position of a point of a plane, we require _________ a) Plane only c) Coordinate geometry b) Two perpendicular lines Answer(b) 9)The abscissa of any point on y-axis is a) 0 b) 1 c) -1 d) any number Answer (a) 10)The ordinate of any point on x-axis is:- a) 0 c) -1 b) 1 d) any number Answer (a)

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