Kumar has a rectangle sketch, which he needs to draw on a coloured paper of length and breadth 32 units and 16 units respectively, using a plotter. Plotter is a device which is attached to a computer like a printer. It is used for drawing complicated sketches. Plotter accepts only positive coordinates where the point (0,0) is the left-bottom corner of the paper. The sketch ABCD needs to be centrally aligned on the paper. Ques. (5) What are the coordinates of A and B respectively?
Answers
Given : coloured paper of length and breadth 32 units and 16 units respectively
To Find : the coordinates of A,B,C and D to be plotted to get the sketch plotted as needed.
The coordinates of A, B
Solution:
Left bottom = (0,0)
Right Top = ( 32, 16)
Sketch 2 is of ABCD centrally aligned on the paper.
Hence O = ( 0 + 32)/2 , ( 0 + 16)/2
= (16,8)
The coordinates of point O in the sketch 2 is (16,8)
(b) The coordinates of A, B, C, D are :
A = 16 - 3 , 8 + 2 = 13 , 10
B = 16 +3 , 8 + 2 = 19 , 10
C = 16 + 3 , 8 - 2 = 19 , 6
D = 16 -3 , 8 - 2 = 13 , 6
(13, 10), (19, 10), (19, 6), (13, 6)
coordinates of A and B are ( 13 , 10) and ( 19 , 10)
c) In the sketch 2, if the point O divides AC in the ratio k : 1 , then the value of k is (ii) 1 ( as Diagonal of rectangle bisect each other)
(d) The point on the y-axis (in sketch 2) which is equidistant from the points B and C is (i) ( 0, 8 )
(e) The point on the x-axis (in sketch 2) which is equidistant from the points C and D is (ii) ( 16, 0 )
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