Tiêu đề 08-Introduction to Graphs(1).pdf ✅

8 CHAPTER INTRODUCTION TO GRAPHS CONTENTS • Introduction to Graphs ➢ INTRODUCTION TO GRAPHS Graphs are visual representation of data collected. It is easier to understand and it is true when there is a comparison to be shown. Graphs are in some different forms like bar graph, pie graph, histogram, line graph etc. (1) A bar graph is used to show comparison among categories & it may consists two or more parallel (vertical or horizontal) bars. (2) A pie chart is used to compare part of a whole, the circle represents the whole. (3) A histogram is a bar graph shows data in intervals and it has adjacent bars over the intervals. There is no gaps between bars since there is no interval between the intervals. (4) A line graph displays data that changes continuously over period of time. It consist some points which joined by consecutive lines. Note : If points are joined by broken line then these type of graphs are called linear graph. 0 5 10 y A B C D x Bar Graph 15 20% D 10% E 10% C 40% A 20% B Pie chart (circle graph) 0 5 10 y 10 20 30 40 x Histogram 15 20 50 60 70 0 5 10 y 5 10 15 20 x Line graph 15 20 25 30 25 0 y A x Linear graph B C D E F The horizontal line is usually called x-axis & vertical line is called y-axis. The intersection point of both perpendicular axis is called origin (0).
Some times a jagged line or kink has been used along horizontal line to indicate that we are not showing some numbers between 0 to first given number. 0 5 10 y 30 35 40 x 15 20 45 50  Coordinates : In a plane we require positions of a point in horizontal & vertical direction (or in x & y direction respectively). These positions are called coordinates or Cartesian coordinates of a point. Eg : If a point covers 3 unit distance in +x direction and 4 units in +y direction then coordinates of point are (3, 4). Here 3 is x coordinate or abscissa and 4 is y coordinate or ordinate. 0 y 3 x 4 (3, 4) Note : These two axes (lines) are perpendicular to each other and divide a paper (plane) in four equal parts, each part is called quadrant. II quadrant III quadrant –x +x +y –y I quadrant IV quadrant O Coordinate of origin O are (0, 0). Coordinate can be +ve or –ve. Sign system in quadrant as follows. (–, +) (–, –) x' x y y' (+, +) (+, –) I IV II III O on x-axis, ordinate (y part) of any point is always 0. Eg. (–5, 0) (2, 0) (7, 0) etc. are on x axis On y axis, abscissa (x part) of any point is always 0. Eg. (0, 7) (0, 3/2) (0, –5) etc are on y axis. Ex.1 Find the location of the following points. (–3, 4), (2, 7), (0, 3), (–5, –2), (3, –8), (–7, –11), (9, 0), (0, 0) Sol. II quadrand, Iq, on y axis, IIIq, IVq, IIIq, on x axis, origin.  Variable : Quantity which change its value according to given condition or a number not having a fix value, called variable like x, y, z, t... Independent and Dependent variable : If one quantity affects the other quantity then first one is called independent variable and other quantity is called dependent variable. (1) Increase of time affects amount of interest. Here time is independent and interest is dependent variable. (2) As speed increases the distance cover in less time. Speed is independent and time is dependent variable. (3) As sides increase of any polygon then perimeter is also increase. Length of sides are independent & perimeter is dependent variable.  Distance from coordinate axis : If a point p(x, y) locate on a plane then distance of this point from x-axis is equal to y coordinate and from y- axis the distance is equal to x coordinate. Note : Distance is always positive O x y y P (x, y) O x y x P (x, y)
IMPORTANT POINTS TO BE REMEMBERED 1. The horizontal line is called x axis. 2. The veritical line is called y axis. 3. The intersection point of both axes is called origin whose coordinates are (0, 0). 4. The ordinate of point which lies on x-axis is always 0. 5. The abscissa of point which lies on y-axis is always 0. 6. For drawing linear graph we have to take suitable scale for both axes. 7. The sum of all angles at centre of circle is equal to 360°. 8. For making pie chart, we find angles for each item by formula 360 ratio of given item × total.
EXERCISE Q.1 Locate the following points on the graph paper A(–3, 4), B(4, 0), C(–5, –3), D(–4, –5), E(0, 5), F(0, –4), G(0, 2), H(–3, 0). Q.2 Mark the following points and join them. Give name and other information about the figure. (i) (–3, 0), (–3, 1), (–3, 2), (–3, 5), (–3, –2) . (ii) (5, 2), (3, 2), (0, 2), (–3, 2), (–1, 2) (iii) (2, –2), (8, 4), (5, 7), (–1, 1) (iv) (1, –2), (3, 6), (5, 10), (3, 2) . (v) (3, 0), (6, 4), (–1, 3) Q.3 Find the distance of the following points from both x and y axis (0, 3), (5, –2), (–3, 4), (7, 3), (8, 17), (15, 3), (7, 7). Q.4 Find the distance of the following points from origin (3, 4), (1, 1), (–5, –12), (9, 40). Q.5 Find the distance between (i) A(–5, 0) and B(7, 0) (ii) P(0, 3) and Q(0, –2) Q.6 Locate the following points on graph paper by taking suitable scale (i) A(15, 25) (ii) B(15, –30) (iii) C(–35, 25) (iv) D(–15, –20) (v) E(–15, 35) (vi) F(25, 15) (vii) G(–5, 0) (viii) H(0, 10) Q.7 In the given line graph, weight of a child according to age is given. Give answers of the following questions. (i) What is the weight of child when age is 3 years. (ii) What is the weight of child when age is 1 year 6 months and 4 years 6 months. (iii) What is the age of child when weight is (1) 6 kg (2) 12 kg (iv) The increase weight between 6 years to 7 years 1 2 3 4 5 6 7 0 3 5 7 9 11 13 y W x eight (in kg) Age (in years) Scale 1 cm = 1 year (x-axis) 1 cm = 2 kg (y-axis) Q.8 The temperature for 6 months of a town as follows : Month Jan. Feb. Mar. April May June Temp. (in oC) 15 18 24 32 39 40 Draw a line graph to represent the above information. Q.9 Draw the line graph to represent the given information. Age (in years) 10 12 14 16 18 20 Weight (in kg) 25 28 33 41 45 56 Q.10 Draw the histogram for the following information and find population of the year 1995. Year 1970 1980 1990 2000 2010 Population (in laks) 16 20 23 27 32 Q.11 The number of workers in a factory as follows : Year 199 8 200 0 200 2 200 4 200 6 200 8 Worker s 220 260 340 480 600 800