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Unit 13 Brain Teaser | Introduction To Graphs | Class-8 DAV Secondary Mathematics
Q1A. Tick () the correct option.
(i) The point at which the x-axis and y-axis intersect on the cartesian plane is
(a) abscissa (h) origin (c) ordinate (d) none
(ii) If a point lies on the y-axis, its coordinates are
(a) (x, 0) (b) (0, 0) (c) (x, y) (d) (0, y)
(iii) The distance of n point P (2, 3) firom x-axis is
(a) 3 units (b) 2 units (c) 5 units (d) 1 unit
(iv) The distance of a point from y-axis is called
(a) ordinate (b) y-coordinate (c) abscissa (d) none
Q1B. Answer the following questions.
(a) Write down the coordinates of the origin.
(b) What are the coordinates of a point which lies on the x-axis?
(c) What is the distance of the point C (4, 2) from y-axis?
(d) What is the distance between the points P (0, 2) and Q (0, 6)?
(e) If the vertices O, A, B of a square OABC are (0, 0), (2, 0) and (2, 2), what are the coordinates of the fourth vertex C of the square.
Q2. Write the coordinates of each of the vertices of each polygon given below:
Q3. The runs scored by the Indian and Australian teams in first 10 overs are given below:
Draw a graph showing the data making the graphs on the same axes in each case.
Answer 3:
HOTS (Higher Order Thinking Skills) Questions
HOTS 1: The perimeter P of an equilateral triangle is given by P = 3s, where s is the side length.
(a) Plot the linear graph between side length (X-axis) and perimeter (Y-axis).
(b) From the graph, find the perimeter when side = 4.5 cm.
(c) From the graph, find the side length when perimeter = 18 cm.
(d) Does the graph pass through the origin? Why?
Solution:
(a) Table of values: (1, 3), (2, 6), (3, 9), (4, 12), (5, 15).
(b) For s = 4.5 cm: P = 3 × 4.5 = 13.5 cm.
(c) For P = 18 cm: s = 18 / 3 = 6 cm.
(d) Yes, the graph passes through the origin (0, 0) because when side length is 0, perimeter is 0 (direct variation with no constant intercept).
HOTS 2: A water tank is filled uniformly by an electric pump at the rate of 15 litres per minute.
(a) Write a linear relation between volume V (in litres) and time t (in minutes).
(b) Find the volume of water filled in 8 minutes.
(c) Find the time required to fill 225 litres.
Solution:
(a) Equation: V = 15t.
(b) For t = 8 min: V = 15 × 8 = 120 litres.
(c) For V = 225 litres: t = 225 / 15 = 15 minutes.
Value Based Questions (VBQs)
Question: A smart city municipal authority installs automated digital water meters that record household water consumption hourly to detect pipeline leakage and promote water conservation.
(a) How can a line graph of hourly consumption detect a water leak?
Solution:
If the line graph shows positive consumption during late night hours (2 AM to 4 AM) when all household appliances are off, it indicates a continuous underground pipe leak.
(b) What value is fostered by monitoring graphical resource usage?
Solution:
Conservation of precious water resources, environmental vigilance, and civic responsibility.
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