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प्रश्न
Sonal and Anmol made a sequence of tile designs from square white tiles surrounding one square purple tile. The purple tiles come in many sizes. Three of the designs are shown below.
(a) Copy and complete the table
| Side Length of Purple Titles | 1 | 2 | 3 | 4 | 5 | 10 | 100 |
| Number of white Tiles in Border |
 |
 |
 |
(b) Draw a graph using the first five pairs of numbers in your table.
(c) Do the points lie on a line?
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उत्तर
(a) In side length 1 the number of white tile surrounding purple tile is 4.
Similarly, in side length 2 the number of white tiles surrounding purple tile is 8.
Thus, we can arrange the following table which shows side length of purple corresponding to the number of white tiles in border.
| Side length of purple | 1 | 2 | 3 | 4 | 5 | 10 | 100 |
| Number of while titles in border | 4 | 8 | 12 | 16 | 20 | 40 | 400 |
Hence, the table shows y = 8x + 16.
(b) On the basis of tables given in sol. (a) part, we draw the following graph
(c) If we join all points in above graph, we get a straight line. This shows, that all points lies on a line.
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संबंधित प्रश्न
Write the coordinates of the vertices of each of these adjoining figures.
A point which lies on both the axis is ______.
______ displays data that changes continuously over periods of time.
All points with y-coordinate as zero lie on the ______.
The x-coordinate of any point lying on the y-axis will be ______.
The ordinate of a point is its distance from the y-axis.
Observe the given graph carefully and complete the table given below.
| x | 1 | 2 | 3 | 4 | 5 |
| y |
This graph shows a map of an island just off the coast of a continent. The point labelled B represents a major city on the coast. The distance between grid lines represents 1 km.
Point A represents a resort that is located 5 km East and 3 km North of Point B. The values 5 and 3 are the coordinates of Point A. The coordinates can be given as the ordered pair (5, 3), where 5 is the horizontal coordinate and 3 is the vertical coordinate.
(i) On a copy of the map, mark the point that is 3 km East and 5 km North of Point B and label it S. Is Point S in the water or on the island? Is Point S in the same place as Point A?
(ii) Mark the point that is 7 km east and 5 km north of Point B and label it C. Then mark the point that is 5 km east and 7 km north of Point B and label it D. Are Points C and D in the same place? Give the coordinates of Points C and D.
(iii) Which point is in the water, (2, 7) or (7, 2)? Mark the point which is in water on your map and label it E.
(iv) Give the coordinates of two points on the island that are exactly 2 km from Point A.
(v) Give the coordinates of the point that is halfway between Points L and P.
(vi) List three points on the island with their x-coordinates greater than 8.
(vii) List three points on the island with a y-coordinate less than 4.
The points on the graph below represent the height and weight of the donkey, dog, crocodile, and ostrich shown in the drawing.
- What are the two variables represented in the graph?
- Which point represents each animals? Explain.
