Coordinate Geometry

Y-axis

X-axis

Let’s refresh our knowledge…

LATITUDEParallel lines which appears horizontal, running from East to West direction

EAST

NORTH

SOUTHLONGITUDEParallel lines which appears vertical, running from North pole to South pole

WEST

LATITUDE

LONGITUDE

EAST

WEST

SOUTH POLE

NORTH POLE

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

COORDINATE GEOMETRY

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

CARTESIAN SYSTEM…

TABLEGLASS

TABLE

GLASS

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

CARTESIAN SYSTEM…

TABLE

GLASS

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

A

4

3

2

1

04321

CO

LU

MN

ROW

Write the name e.g.:- ‘A’ is sitting on desk lying in 2nd row and 4th column ( 4,2)

This activity gives you a

brief idea of Cartesian System.

DESK

Name of the student occupying the desk

COORDINATE AXES…

ORIGIN is the Point of Intersection ‘O’

y1

x1

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

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”.

SOME 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

0X1X

Y1

Y

-1-2-3-4-5-6

1 2 3 4 5 6

6 54321

-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

Quadrant 2

XX1

Y1

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)

QUADRANTS…

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

(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

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

(0,4)

SOME ILLUSTRATIONS…

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

Answers i) As abscissa is negative and ordinate is positive so (-3, 2) lies in Quadrant 2ii) 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 .

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 XOX1 (X – axis), vertical line as YOY1, (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) .

1234

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) 6Answer (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) 00 b) 900 c) 1800 d) 3600

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)

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 geometryb) 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) -1b) 1 d) any number

Answer (a)

Thanks…

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