Rayat Shikshan Sanstha Satara Chhatrapati Shivaji Vidyalaya Ganore

Rayat Shikshan Sanstha, Satara Chhatrapati Shivaji Vidyalaya, Ganore STD-IX ALGEBRA (Upgrade Unit – 5 GRAPHS Std-9 th Sub-Mathematics Chapt. -Graphs

Rayat Shikshan Sanstha, Satara Chhatrapati Shivaji Vidyalaya, Ganore Sub-units(Index): - 5. 1 Cartesian coordinate system • Coordinate axis • Origin • Quadrants • Cartesian coordinate of a point in a plane • Coordinates of points on axes • Points in quadrants and sign convention • Plotting the points in a Cartesian plane 5. 2 Graphs of lines parallel to axes • Equation of lines parallel to X-axis • Equation of lines parallel to Y-axis • Equation of X-axis • Equation of Y-axis 5. 3 Graph of equation ax + by +c = 0 Std-9 th Sub-Mathematics Chapt. -Graphs

Rayat Shikshan Sanstha, Satara Chhatrapati Shivaji Vidyalaya, Ganore Newly added subunit • Graph of equation ax + by + c = 0 Std-9 th Sub-Mathematics Chapt. -Graphs

Rayat Shikshan Sanstha, Satara Chhatrapati Shivaji Vidyalaya, Ganore Introduction Strategy – Problem solving method To find out location of a point on blackboard. To find out friends house. Location of a student in the classroom. To find a seat in cinema hall. To locate the brinjal plant in farm. Std-9 th Sub-Mathematics Chapt. -Graphs

Rayat Shikshan Sanstha, Satara Chhatrapati Shivaji Vidyalaya, Ganore RENE DESCARTES The French Mathematician Rene Descartes (1596 -1650) one day , when restingin bed, he noticed the movement of an insect near a corner of the cieling and began to think of determining the position of a given point in a plane. His system of fixing a point with the help of two measurements, vertical & horrizontal, came to be known as Cartesian System in his honour Std-9 th Sub-Mathematics Chapt. -Graphs

Rayat Shikshan Sanstha, Satara Chhatrapati Shivaji Vidyalaya, Ganore Cartesian Coordinate System Y Positive direction of Y -axis Positive direction of X-axis X X’ O Negative direction of X-axis Negative direction of Y-axis Y’ Std-9 th Sub-Mathematics Chapt. -Graphs

Rayat Shikshan Sanstha, Satara Chhatrapati Shivaji Vidyalaya, Ganore Quadrants Y SECOND QUADRANT FIRST QUADRANT X X’ O THIRD QUADRANT Y’ Std-9 th Sub-Mathematics FOURTH QUADRANT Chapt. -Graphs

Rayat Shikshan Sanstha, Satara Chhatrapati Shivaji Vidyalaya, Ganore Cartesian Coordinate of a point in a plane Distance of a point from Y-axis Y P (5 , 3) Distance of a point from X-axis X X’ O Std-9 th Y’ Sub-Mathematics Chapt. -Graphs

Rayat Shikshan Sanstha, Satara Chhatrapati Shivaji Vidyalaya, Ganore Coordinates of a point in a plane: • X-coordinate – Perpendicular distance of a point from Y-axis is called as x-coordinate or abscissa. • Y-coordinate- Perpendicular distance of a point from X-axis is called as y-coordinate or ordinate. Std-9 th Sub-Mathematics Chapt. -Graphs

Rayat Shikshan Sanstha, Satara Chhatrapati Shivaji Vidyalaya, Ganore Coordinates of points on axes: • y-coordinate of every point on X-axis is zero , why? • x-coordinate of every point on Y-axis is zero , why? • What are the coordinates of origin? Std-9 th Sub-Mathematics Chapt. -Graphs

Rayat Shikshan Sanstha, Satara Chhatrapati Shivaji Vidyalaya, Ganore Points in first quadrant: Points Coordinates Sign of coordinates Sign of x y coordinates A (2 , 3 ) + + ( + , + ) G (5 , 4 ) + + ( + , + ) L (7 , 8 ) + + ( + , + ) Q (1 , 7 ) + + ( + , + ) T (9 , 3 ) + + ( + , + ) Std-9 th Sub-Mathematics Chapt. -Graphs

Rayat Shikshan Sanstha, Satara Chhatrapati Shivaji Vidyalaya, Ganore Quadrants Y SECOND QUADRANT FIRST QUADRANT (+ , +) (- , +) X’ O FOURTH QUADRANT THIRD QUADRANT (- , -) Y’ Std-9 th Sub-Mathematics (- , -) Chapt. -Graphs X

Rayat Shikshan Sanstha, Satara Scale 1 cm=1 unit On both the axes Chhatrapati Shivaji Vidyalaya, Ganore Observe and write the Y positions of the points 4 3 A Q 2 1 X’ on X axes Point M lies ………. . D Point G lies ………. . in IV quadrant M 0 -6 -5 -4 -3 -2 -1 0 -1 Y axes Point T lies on ………. . 1 2 3 4 T 5 6 X Point Q lies ………. . in I quadrant Point D lies ………. . in I quadrant -2 B -3 -4 Std-9 th in III quadrant Point B lies ………. . G in II quadrant Point A lies ………. . Y’ Sub-Mathematics Chapt. -Graphs

Rayat Shikshan Sanstha, Satara Chhatrapati Shivaji Vidyalaya, Ganore Points in quadrants & sign convention Region Quadrant Nature of x & y Signs of coordinates XOY I X>0 , y>0 (+, +) YOX’ II X<0 , y>0 (-, +) X’OY’ III X<0 , y<0 ( -, - ) Y’OX IV X>0 , y<0 (+, -) Std-9 th Sub-Mathematics Chapt. -Graphs

Rayat Shikshan Sanstha, Satara Chhatrapati Shivaji Vidyalaya, Ganore In which quadrant or on axis do the following points lie? Point (-2, 4) In II quadrant Point (3, -5) In IV quadrant Point (0, 6) On Y-axis Point (-2, -4) In III quadrant Point (-7, 0) Std-9 th On X-axis Sub-Mathematics Chapt. -Graphs

Rayat Shikshan Sanstha, Satara Chhatrapati Shivaji Vidyalaya, Ganore 5. 2 GRPHS OF Lines parallel to axis Scale 1 cm=1 unit On both the axes Line AB 4 3 Line CD 2 1 X’ -6 -5 -4 -3 -2 -1 0 1 Points on line (-6, 4), (-4, 4), (-1, 4), (0, 4), (3, 4) Line. CD (-5, 2), (-2, 2), (0, 2), (4, 2), (6, 2) Line EF (-6, -3), (-3, -3), (-1, 3), (3, -3), (6, -3) Line. GH 2 3 4 5 6 X (-7, - 4), (-4, - 4), (0, 4), (3, - 4), (7, - 4) -1 X-axis -2 -3 Std-9 th -4 (-6, 0) , (-4, 0), (1, 0), (4, 0), (6, 0) Line GH Sub-Mathematics Chapt. -Graphs

Rayat Shikshan Sanstha, Satara Chhatrapati Shivaji Vidyalaya, Ganore Responses • Every point lies on line AB has Y-coordinate same and that is 4 which is constant. • Every point on the line AB is equidistant from Xaxis that is 4 unit. So line AB is parallel to X-axis. • Equation of line AB is y = 4. Simillarly, • Equation of line CD is y = 2. • Equation of line EF is y = -3. • Equation of line GH is y = -4. • Equation of line parallel to x-axis is y = b (constant) Std-9 th Sub-Mathematics Chapt. -Graphs

Rayat Shikshan Sanstha, Satara Chhatrapati Shivaji Vidyalaya, Ganore WHY ? Equation of lines parallel to Y-axis is x = a ( constant) Std-9 th Sub-Mathematics Chapt. -Graphs

Rayat Shikshan Sanstha, Satara Chhatrapati Shivaji Vidyalaya, Ganore Equation of axes: WHY? • Equation of x- axis is y = 0. • Equation of Y- axis is x = 0. Std-9 th Sub-Mathematics Chapt. -Graphs

Rayat Shikshan Sanstha, Satara Chhatrapati Shivaji Vidyalaya, Ganore The line y = b lies above or below the Xaxis according as b is positive or negative. n. The x = a lies to the right or left of Y-axis according as a is positive or negative. n. A horizontal line has no Xintercept and vertical line has no Y -intercept. Std-9 th Sub-Mathematics Chapt. -Graphs

Rayat Shikshan Sanstha, Satara Chhatrapati Shivaji Vidyalaya, Ganore Graph of equation ax+by+c = 0 Steps for plotting the graph of Equation ax+by+c=0 • Express y in terms of x. • Choose at least two convenient values of x and find the corresponding values of y , satisfying the given equation. • Write these values of x and y in ordered pair (x, y). • Plot the ordered pair (x, y)on a graph. • Join these points by straight line and extend it in both the directions. • The line is the graph of the eqution ax + by + c = 0 Std-9 th Sub-Mathematics Chapt. -Graphs

Rayat Shikshan Sanstha, Satara Chhatrapati Shivaji Vidyalaya, Ganore Responses • Coordinates of points lies on line ax+by+c=0 are the solution of the equation ax+by+c=0. • The points on the line ax+by+c=0 are colinear. Std-9 th Sub-Mathematics Chapt. -Graphs

Rayat Shikshan Sanstha, Satara Chhatrapati Shivaji Vidyalaya, Ganore OPEN ENDED QUESTIONS • 1. Write any three points lies on the line x=5. • 2. Write the coordinates of any three points lies on the line y = -4. • 3. Write any two points lies in the first quadrant. • 4. Write y-coordinate of points whose x-coordinate is 7. • 5. Write x coordinate of any point whose y coordinate is -6. • 6. Write the coordinates of any three points lies on the line x+y=5. Std-9 th Sub-Mathematics Chapt. -Graphs

Rayat Shikshan Sanstha, Satara Chhatrapati Shivaji Vidyalaya, Ganore Draw the graphs of following equations on same coordinate system. Scale 1 cm=1 unit On both the axes Y 4 y=x 3 2 1 X’ -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 X -1 y= -x -2 -3 -4 Std-9 th Y’ Sub-Mathematics Chapt. -Graphs

Rayat Shikshan Sanstha, Satara Chhatrapati Shivaji Vidyalaya, Ganore 1) 2) 3) 4) Std-9 th y=x y=-x y=2 x y=-2 x Sub-Mathematics x 2 -4 1 y 2 -4 1 (x, y) (2, 2) (-4, -4) (1, 1) x 2 -4 1 y -2 4 -1 (x, y) (2, -2) x 2 -4 1 y 4 -8 2 (x, y) (2, 4) (-4, 4) (1, -1) (-4, -8) (1, 2) x 2 -4 1 y -4 8 -2 (x, y) (2, -4) (-4, 8) (1, -2) Chapt. -Graphs

THANK YOU