Page 1 1. Plot the points (5, 0), (5, 1), (5, 8). Do they lie on a line? What is your observation? Solution: Take a point O on the graph paper and draw horizontal and vertical lines OX and OY respectively. Then, let on the xaxis and yaxis 1 cm represents 1 unit. To plot point (5, 0), we start from the origin O and move 5 cm along X  axis. The point we arrive at is point (5, 0). To plot point (5, 1), we move 5 cm along X  axis and 1 cm along Y  axis. The point we arrive at is point (5, 1). To plot point (5, 8), we move 5 cm along X  axis and 8 cm along Y  axis. The point we arrive at is point (5, 8). From the above graph, we observe that all points are having same X – coordinates, it can be seen that the points lie on a line parallel to the yaxis. Hence all points lie on the same line. 2. Plot the points (2, 8), (7, 8) and (12, 8). Join these points in pairs. Do they lie on a line? What do you observe? Solution: Take a point O on the graph paper and draw the horizontal and vertical lines OX and OY Page 2 1. Plot the points (5, 0), (5, 1), (5, 8). Do they lie on a line? What is your observation? Solution: Take a point O on the graph paper and draw horizontal and vertical lines OX and OY respectively. Then, let on the xaxis and yaxis 1 cm represents 1 unit. To plot point (5, 0), we start from the origin O and move 5 cm along X  axis. The point we arrive at is point (5, 0). To plot point (5, 1), we move 5 cm along X  axis and 1 cm along Y  axis. The point we arrive at is point (5, 1). To plot point (5, 8), we move 5 cm along X  axis and 8 cm along Y  axis. The point we arrive at is point (5, 8). From the above graph, we observe that all points are having same X – coordinates, it can be seen that the points lie on a line parallel to the yaxis. Hence all points lie on the same line. 2. Plot the points (2, 8), (7, 8) and (12, 8). Join these points in pairs. Do they lie on a line? What do you observe? Solution: Take a point O on the graph paper and draw the horizontal and vertical lines OX and OY respectively. Then, let on the xaxis and y axis 1 cm represents 1 unit. In order to plot point (2, 8), we start from the origin O and move 8 cm along X  axis. The point we arrive at is (2, 8). To plot point (7, 8), we move 7 cm along X  axis and 8 cm along Y  axis. The point we arrive at is (7, 8). To plot point (12, 8), we move 12 cm along X  axis and 8 cm along Y  axis. The point we arrive at is (12, 8). From the above graph, we observe that all points are having same Y – coordinates, it can be seen that the points lie on a line parallel to the xaxis. Hence all points lie on the same line. 3. Locate the points : (i) (1, 1), (1, 2), (1, 3), (1, 4) (ii) (2, 1), (2, 2), (2, 3), (2, 4) (iii) (1, 3), (2, 3), (3, 3), (4, 3) (iv) (1, 4), (2, 4), (3, 4), (4, 4,) Solution: (i) (1, 1), (1, 2), (1, 3), (1, 4) To plot these points, Take a point O on a graph paper and draw horizontal and vertical lines OX and OY respectively. Then, let on xaxis and yaxis 1 cm represents 1 unit. Page 3 1. Plot the points (5, 0), (5, 1), (5, 8). Do they lie on a line? What is your observation? Solution: Take a point O on the graph paper and draw horizontal and vertical lines OX and OY respectively. Then, let on the xaxis and yaxis 1 cm represents 1 unit. To plot point (5, 0), we start from the origin O and move 5 cm along X  axis. The point we arrive at is point (5, 0). To plot point (5, 1), we move 5 cm along X  axis and 1 cm along Y  axis. The point we arrive at is point (5, 1). To plot point (5, 8), we move 5 cm along X  axis and 8 cm along Y  axis. The point we arrive at is point (5, 8). From the above graph, we observe that all points are having same X – coordinates, it can be seen that the points lie on a line parallel to the yaxis. Hence all points lie on the same line. 2. Plot the points (2, 8), (7, 8) and (12, 8). Join these points in pairs. Do they lie on a line? What do you observe? Solution: Take a point O on the graph paper and draw the horizontal and vertical lines OX and OY respectively. Then, let on the xaxis and y axis 1 cm represents 1 unit. In order to plot point (2, 8), we start from the origin O and move 8 cm along X  axis. The point we arrive at is (2, 8). To plot point (7, 8), we move 7 cm along X  axis and 8 cm along Y  axis. The point we arrive at is (7, 8). To plot point (12, 8), we move 12 cm along X  axis and 8 cm along Y  axis. The point we arrive at is (12, 8). From the above graph, we observe that all points are having same Y – coordinates, it can be seen that the points lie on a line parallel to the xaxis. Hence all points lie on the same line. 3. Locate the points : (i) (1, 1), (1, 2), (1, 3), (1, 4) (ii) (2, 1), (2, 2), (2, 3), (2, 4) (iii) (1, 3), (2, 3), (3, 3), (4, 3) (iv) (1, 4), (2, 4), (3, 4), (4, 4,) Solution: (i) (1, 1), (1, 2), (1, 3), (1, 4) To plot these points, Take a point O on a graph paper and draw horizontal and vertical lines OX and OY respectively. Then, let on xaxis and yaxis 1 cm represents 1 unit. To plot point (1, 1), we start from the origin O and move 1 cm along X  axis and 1 cm along Y  axis. The point we arrive at is (1, 1). To plot point (1, 2), we move 1 cm along X  axis and 2 cm along Y  axis. The point we arrive at is (1, 2). To plot point (1, 3), we move 1 cm along X  axis and 3 cm along Y  axis. The point we arrive at is (1, 3). To plot point (1, 4), we move 1 cm along X  axis and 4 cm along Y  axis. The point we arrive at is (1, 4) (ii) (2, 1), (2, 2), (2, 3), (2, 4) To plot these points, Take a point O on a graph paper and draw horizontal and vertical lines OX and OY respectively. Then, let on xaxis and yaxis 1 cm represents 1 unit. To plot point (2, 1), we move 2 cm along X  axis and 1 cm along Y  axis. The point we arrive at is (2, 1). To plot point (2, 2), we move 2 cm along X  axis and 2 cm along Y  axis. The point we arrive at is (2, 2). To plot point (2, 3), we move 2 cm along X  axis and 3 cm along Y  axis. The point we arrive at is (2, 3). To plot point (2, 4), we move 2 cm along X  axis and 4 cm along Y  axis. The point we arrive at is (2, 4). Page 4 1. Plot the points (5, 0), (5, 1), (5, 8). Do they lie on a line? What is your observation? Solution: Take a point O on the graph paper and draw horizontal and vertical lines OX and OY respectively. Then, let on the xaxis and yaxis 1 cm represents 1 unit. To plot point (5, 0), we start from the origin O and move 5 cm along X  axis. The point we arrive at is point (5, 0). To plot point (5, 1), we move 5 cm along X  axis and 1 cm along Y  axis. The point we arrive at is point (5, 1). To plot point (5, 8), we move 5 cm along X  axis and 8 cm along Y  axis. The point we arrive at is point (5, 8). From the above graph, we observe that all points are having same X – coordinates, it can be seen that the points lie on a line parallel to the yaxis. Hence all points lie on the same line. 2. Plot the points (2, 8), (7, 8) and (12, 8). Join these points in pairs. Do they lie on a line? What do you observe? Solution: Take a point O on the graph paper and draw the horizontal and vertical lines OX and OY respectively. Then, let on the xaxis and y axis 1 cm represents 1 unit. In order to plot point (2, 8), we start from the origin O and move 8 cm along X  axis. The point we arrive at is (2, 8). To plot point (7, 8), we move 7 cm along X  axis and 8 cm along Y  axis. The point we arrive at is (7, 8). To plot point (12, 8), we move 12 cm along X  axis and 8 cm along Y  axis. The point we arrive at is (12, 8). From the above graph, we observe that all points are having same Y – coordinates, it can be seen that the points lie on a line parallel to the xaxis. Hence all points lie on the same line. 3. Locate the points : (i) (1, 1), (1, 2), (1, 3), (1, 4) (ii) (2, 1), (2, 2), (2, 3), (2, 4) (iii) (1, 3), (2, 3), (3, 3), (4, 3) (iv) (1, 4), (2, 4), (3, 4), (4, 4,) Solution: (i) (1, 1), (1, 2), (1, 3), (1, 4) To plot these points, Take a point O on a graph paper and draw horizontal and vertical lines OX and OY respectively. Then, let on xaxis and yaxis 1 cm represents 1 unit. To plot point (1, 1), we start from the origin O and move 1 cm along X  axis and 1 cm along Y  axis. The point we arrive at is (1, 1). To plot point (1, 2), we move 1 cm along X  axis and 2 cm along Y  axis. The point we arrive at is (1, 2). To plot point (1, 3), we move 1 cm along X  axis and 3 cm along Y  axis. The point we arrive at is (1, 3). To plot point (1, 4), we move 1 cm along X  axis and 4 cm along Y  axis. The point we arrive at is (1, 4) (ii) (2, 1), (2, 2), (2, 3), (2, 4) To plot these points, Take a point O on a graph paper and draw horizontal and vertical lines OX and OY respectively. Then, let on xaxis and yaxis 1 cm represents 1 unit. To plot point (2, 1), we move 2 cm along X  axis and 1 cm along Y  axis. The point we arrive at is (2, 1). To plot point (2, 2), we move 2 cm along X  axis and 2 cm along Y  axis. The point we arrive at is (2, 2). To plot point (2, 3), we move 2 cm along X  axis and 3 cm along Y  axis. The point we arrive at is (2, 3). To plot point (2, 4), we move 2 cm along X  axis and 4 cm along Y  axis. The point we arrive at is (2, 4). (iii) (1, 3), (2, 3), (3, 3), (4, 3) To plot these points, Take a point O on a graph paper and draw horizontal and vertical lines OX and OY respectively. Then, let on xaxis and yaxis 1 cm represents 1 unit. To plot point (1, 3), we move 1 cm along X  axis and 3 cm along Y  axis. The point we arrive at is (1, 3). To plot point (2, 3), we move 2 cm along X  axis and 3 cm along Y  axis. The point we arrive at is (2, 3). To plot point (3, 3), we move 3 cm along X  axis and 3 cm along Y  axis. The point we arrive at is (3, 3). To plot point (4, 3), we move 4 0cm along X  axis and 3 cm along Y  axis. The point we arrive at is (4, 3). Page 5 1. Plot the points (5, 0), (5, 1), (5, 8). Do they lie on a line? What is your observation? Solution: Take a point O on the graph paper and draw horizontal and vertical lines OX and OY respectively. Then, let on the xaxis and yaxis 1 cm represents 1 unit. To plot point (5, 0), we start from the origin O and move 5 cm along X  axis. The point we arrive at is point (5, 0). To plot point (5, 1), we move 5 cm along X  axis and 1 cm along Y  axis. The point we arrive at is point (5, 1). To plot point (5, 8), we move 5 cm along X  axis and 8 cm along Y  axis. The point we arrive at is point (5, 8). From the above graph, we observe that all points are having same X – coordinates, it can be seen that the points lie on a line parallel to the yaxis. Hence all points lie on the same line. 2. Plot the points (2, 8), (7, 8) and (12, 8). Join these points in pairs. Do they lie on a line? What do you observe? Solution: Take a point O on the graph paper and draw the horizontal and vertical lines OX and OY respectively. Then, let on the xaxis and y axis 1 cm represents 1 unit. In order to plot point (2, 8), we start from the origin O and move 8 cm along X  axis. The point we arrive at is (2, 8). To plot point (7, 8), we move 7 cm along X  axis and 8 cm along Y  axis. The point we arrive at is (7, 8). To plot point (12, 8), we move 12 cm along X  axis and 8 cm along Y  axis. The point we arrive at is (12, 8). From the above graph, we observe that all points are having same Y – coordinates, it can be seen that the points lie on a line parallel to the xaxis. Hence all points lie on the same line. 3. Locate the points : (i) (1, 1), (1, 2), (1, 3), (1, 4) (ii) (2, 1), (2, 2), (2, 3), (2, 4) (iii) (1, 3), (2, 3), (3, 3), (4, 3) (iv) (1, 4), (2, 4), (3, 4), (4, 4,) Solution: (i) (1, 1), (1, 2), (1, 3), (1, 4) To plot these points, Take a point O on a graph paper and draw horizontal and vertical lines OX and OY respectively. Then, let on xaxis and yaxis 1 cm represents 1 unit. To plot point (1, 1), we start from the origin O and move 1 cm along X  axis and 1 cm along Y  axis. The point we arrive at is (1, 1). To plot point (1, 2), we move 1 cm along X  axis and 2 cm along Y  axis. The point we arrive at is (1, 2). To plot point (1, 3), we move 1 cm along X  axis and 3 cm along Y  axis. The point we arrive at is (1, 3). To plot point (1, 4), we move 1 cm along X  axis and 4 cm along Y  axis. The point we arrive at is (1, 4) (ii) (2, 1), (2, 2), (2, 3), (2, 4) To plot these points, Take a point O on a graph paper and draw horizontal and vertical lines OX and OY respectively. Then, let on xaxis and yaxis 1 cm represents 1 unit. To plot point (2, 1), we move 2 cm along X  axis and 1 cm along Y  axis. The point we arrive at is (2, 1). To plot point (2, 2), we move 2 cm along X  axis and 2 cm along Y  axis. The point we arrive at is (2, 2). To plot point (2, 3), we move 2 cm along X  axis and 3 cm along Y  axis. The point we arrive at is (2, 3). To plot point (2, 4), we move 2 cm along X  axis and 4 cm along Y  axis. The point we arrive at is (2, 4). (iii) (1, 3), (2, 3), (3, 3), (4, 3) To plot these points, Take a point O on a graph paper and draw horizontal and vertical lines OX and OY respectively. Then, let on xaxis and yaxis 1 cm represents 1 unit. To plot point (1, 3), we move 1 cm along X  axis and 3 cm along Y  axis. The point we arrive at is (1, 3). To plot point (2, 3), we move 2 cm along X  axis and 3 cm along Y  axis. The point we arrive at is (2, 3). To plot point (3, 3), we move 3 cm along X  axis and 3 cm along Y  axis. The point we arrive at is (3, 3). To plot point (4, 3), we move 4 0cm along X  axis and 3 cm along Y  axis. The point we arrive at is (4, 3). (iv) (1, 4), (2, 4), (3, 4), (4, 4,) To plot these points, Take a point O on a graph paper and draw horizontal and vertical lines OX and OY respectively. Then, let on xaxis and yaxis 1 cm represents 1 unit. In order to plot point (1, 4), we move 1 cm along X  axis and 4 cm along Y  axis. The point we arrive at is (1, 4). To plot point (2, 4), we move 2 cm along X  axis and 4 cm along Y  axis. The point we arrive at is (2, 4). To plot point (3, 4), we move 3 cm along X  axis and 4 cm along Y axis. The point we arrive at is (3, 4). To plot point (4, 4), we move 4 cm along X  axis and 4 cm along Y  axis. The point we arrive at is (4, 4). 4. Find the coordinates of points A, B, C, D in Fig. 27.7Read More
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