Here we will learn how to solve different types of problems on plotting points in the xy plane.
1. Plot the points in the same figure.
(i) (3, 1), (ii) (5, 0), (iii) (3, 4.5), (iv) (1, 6), (v) (2.5, 1.5)
Solution:
Draw two mutually perpendicular lines X’OX and Y’OY which are the x and y axes respectively.
Indicate the numbers (on a certain scale) on both the lines with O and 0.
(i) Let A = (3, 1). Here the xcoordinate = 3 and
ycoordinate = 1. So, move 3 units from O towards the positive direction of
the xaxis. From that place move 1 unit towards the negative direction of the
yaxis. The position of the point now reached has the coordinates (3, 1).
(ii) Let B = (5, 0). Here, the xcoordinate = 5 and the ycoordinate = 0. So, the point is on the xaxis. Move 5 units from O towards the negative direction of the xaxis. The position of the point reached has the coordinates (5, 0).
(iii) Let C = (3, 4.5). Here, the xcoordinate = 3 and the
ycoordinate = 4.5. So, move 3 units from O towards the positive direction of
the xaxis. From that place move 4.5 units towards the positive direction of
the yaxis. The position of the point now reached has the coordinates (3, 4.5).
(iv) Let D = (1, 6). Here, the xcoordinate = 1 and the ycoordinate = 6. So, move 1 unit from O towards the negative direction of the xaxis. From that place move 6 units towards the positive direction of the yaxis. The position of the point now reached has the coordinates (1, 6).
(v) Let E = (2.5, 1.5). Here, the xcoordinate = 2.5 and the ycoordinate = 1.5. So, move 2.5 units from O towards the negative direction of the xaxis. From that place move 1.5 units towards the negative direction of the yaxis. The position of the point now reached has the coordinates (2.5, 1.5).
2. Plot the points (12, 8) and (16, 20) in the xy plane.
Solution:
Taking 1 cm = 4 as the scale of representation the points are plotted as shown below.
(i) Let P = (12, 8). Here the xcoordinate = 12 and ycoordinate = 8. So, move 12 units from O towards the positive direction of the xaxis. From that place move 8 units towards the negative direction of the yaxis. The position of the point now reached has the coordinates (12, 8).
(ii) Let Q = (16, 20). Here, the xcoordinate = 16 and the ycoordinate = 20. So, move 16 units from O towards the negative direction of the xaxis. From that place move 20 units towards the negative direction of the yaxis. The position of the point now reached has the coordinates (16, 20).
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