Mathematics
In each of the following, the co-ordinates of the three vertices of a rectangle ABCD are given. By plotting the given points; find, in each case, the co-ordinates of the fourth vertex :
(i) A (2, 0), B (8, 0) and C (8, 4).
(ii) A (4, 2), B (-2, 2) and D (4, -2).
(iii) A (- 4, - 6), C (6, 0) and D (- 4, 0)
(iv) B (10, 4), C (0, 4) and D (0, - 2).
Coordinate Geometry
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Answer
(i) After plotting the given points A(2, 0), B(8, 0) and C(8, 4) on a graph paper, join A with B and B with C. From the graph, it is clear that the vertical distance between the points B(8, 0) and C(8, 4) is 4 units. Therefore, the vertical distance between points A(2, 0) and D must be 4 units.
Now, complete the rectangle ABCD and read the coordinates of point D. As shown on the graph, D = (2, 4).
Hence, D = (2, 4).
(ii) After plotting the given points A(4, 2), B(-2, 2) and D(4, -2) on a graph paper, join A with B and A with D.
From the graph it is clear that the vertical distance between the points A(4, 2) and D(4, -2) is 4 units and the horizontal distance between the points A(4, 2) and B(-2, 2) is 6 units. Therefore, the vertical distance between points B(-2, 2) and C must be 4 units and the horizontal distance between points B(-2, 2) and C must be 6 units.
Now, complete the rectangle ABCD and read the coordinates of point C. As shown on the graph, C = (-2, 2).
Hence, C = (-2, 2).
(iii) After plotting the given points A(-4, -6), C(6, 0) and D(-4, 0) on a graph paper, join A with D and C with D.
From the graph it is clear that the vertical distance between the points A(-4, -6) and D(-4, 0) is 6 units and the horizontal distance between the points C(6, 0) and D(-4, 0) is 10 units. Therefore, the vertical distance between the points A(-4, -6) and B must be 10 units and the horizontal distance between the points C(6, 0) and B must be 10 units.
Now complete the rectangle ABCD and read the coordinates of point B. As shown on the graph, B = (6, -6).
Hence, B = (6, -6).
(iv) After plotting the given points B (10, 4), C (0, 4) and D (0, - 2) on a graph paper, join B with C and C with D.
From the graph it is clear that the vertical distance between the points C(0, 4) and D(0, -2) is 6 units and the horizontal distance between the points C(0, 4) and D(0, -2) is 10 units. Therefore, the vertical distance between the points B(10, 4) and A must be 6 units and the horizontal distance between the points D(0, -2) and B must be 10 units.
Now complete the rectangle ABCD and read the coordinates of point A. As shown on the graph, A = (10, -2).
Hence, A = (10, -2).
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