Introduction to coordinate geometry by Pratima Nayak

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This can be used by the teacher to introduce Coordinate Geometry in Secondary level.

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How much is the distance between flower and the butterfly ?

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CARTISIAN SYSTEM OF RECTANGULAR CO-0RDINATES

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-5 -4 -3 -2 -1 0 1 2 3 4 5 6 x- axis HORINZENTAL LINE IS CALLED X-AXIS

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-5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Origin (0,0) x- axis Y- axis HORINZENTAL LINE IS CALLED X-AXIS VERTICAL LINE IS CALLED Y-AXIS

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-5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 1 st quadrant

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-5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 1 st quadrant 2nd quadrant

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-5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 1 st quadrant 2nd quadrant 3rd quadrant 4th quadrant

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(3, 0) To mark a point on a plane (3, 0) -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

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(-5, 0) To mark a point on a plane (-5, 0) -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

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( 0,3) To mark a point on a plane ( 0,3) -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

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( 0,-1) To mark a point on a plane ( 0,-1) -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

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What are the co-ordinates of A ? -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 A

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(4, 2) To mark a point on a plane (4, 2 ) 4 is x coordinate or abscissa 2 is y coordinate or ordinate . -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

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(3,3) To mark a point on a plane (3,3 ) -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

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(3,3) -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 1 st quadrant IN IST QUADRANT BOTH THE CO-ORDINATES ARE POSITIVE.

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(-3,3) To mark a point on a plane (-3,3 ) -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

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(-3,3) -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 2nd quadrant IN 2ND QUADRANT ABSCISSA IS NEGATIVE AND ORDINATES IS POSITIVE.

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(-4,-2) To mark a point on a plane (-4,-2) -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

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(-4,-2) -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 3rd quadrant IN 3RD QUADRANT BOTH THE CO-ORDINATES ARE NEGATIVE.

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(3,-2) To mark a point on a plane (3,-2) -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

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(3,-2) -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 4th quadrant IN 4TH QUADRANT ABSCISSA IS POSITIVE AND ORDINATES IS NEGATIVE.

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-5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 What is the coordinates of shown point? (-3,-1)

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-5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 What is the coordinates of shown point?

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-5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 What is the coordinates of shown point?

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-5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 A B C What are the coordinates of vertices of the triangle?

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-5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 What are the coordinates of vertices of the star?

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(0,0) (3,3) To mark a point on a plane (3,3 ) Let there is a flower at this point. -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

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(0,0) (1,1) Let there is a butterfly at (1,1) (3,3)

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How much is the distance between flower and the butterfly ? (1,1) (3,3)

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A B Let A is the position of the Butterfly.A has co-ordinates (1,1). B is the position of the flower.B has the coordinate ( 3, 3). (1,1) (3,3) O

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A B Let us draw the perpendiculars AP on X axis ,BQ on Y axis. AC on BQ to complete a right triangle ABC. (1,1) (3,3) P Q C O

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A B In Triangle ABC , the length of AC = PQ PQ = OQ – OP =3 – 1 =2 (1,1) (3,3) P Q C O the length of BC =BQ - CQ =3 – 1 =2 In Right Triangle ABC ,

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How much is the distance between the points A and B ? A B O

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A B C Perpendiculars AP and BQ on X axis are drawn.. AC on BQ are drawn to complete a right triangle ABC. P Q O

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A B C P O Q OP = x 1 PQ = x 2 - x 1 OQ = x 2 AC = x 2 - x 1 BC = y 2 - y 1 BQ = y 2 OQ = y 1

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A B C . AC = BC = O P Q

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A B C O P Q AC = BC =

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The distance between the points A and B A B O It is called distance formula .

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A B O C is a point on the line joining A and B in ratio m:n

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A B C C is a point on the line joining A and B in ratio m:n What will be co-ordinates of C? m n

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A B C Perpendiculars AM,CN , BP AR CS Are drawn. O M N P Q R S m n

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A B C Triangle ACQ and BCS are similar . O M N P Q R S m n

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A B C Triangle ACQ and BCS are similar . O M N P Q R S m n

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A B C C is a point on the line joining A and B in ratio m:n The co-ordinates of C are : m n This is called section formula

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A B C C is an exterior point point on the line joining A and B in ratio m:n The co-ordinates of C are : m n

Co-ordinates of circumcentre OF A TRIANGLE WHEN VERTICES ARE GIVEN:

Co-ordinates of circumcentre OF A TRIANGLE WHEN VERTICES ARE GIVEN A B C 0

Co-ordinates of in -centre OF A TRIANGLE WHEN VERTICES ARE GIVEN:

Co-ordinates of in -centre OF A TRIANGLE WHEN VERTICES ARE GIVEN A B C 0 c a b

ASSIGNMENT:

ASSIGNMENT Q1.Which point on x axis is equidistant from (5,9) and (-4,6)? Q2. Which point on y axis is equidistant from (2,3) and (-4,1)?

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ASSIGNMENT Q3.Prove that (2a,4a),(2a,6a)and (2a+ 3a) are vertices of an equilateral triangle. Q4.In what ratio the x-axis divide the line segment joining the points (2,-3) and (5,6)?

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ASSIGNMENT Q5. For what value of x will the points (x,1),(2,1) and (4,5) lie on a line? Q6. Determine the ratio in which the line 3x+y-9=0 divides the segment joining the points (1,3) and (2,7)?

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ASSIGNMENT Q7If the points (-2,-1), (1,0),(x,3) and ( 1,y) form a parallelogram, find the value of x and y. Q8.Find the coordinates of (i) centroid ii)incentre (iii)circumcentre of of the triangle whose vertices are (0,6),(8,12) and ( 8,0)

Thank You:

Thank You Developed by Pratima Nayak, Kendriya Vidyalaya,Fort Willia,Kolkata

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