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Question
Let ABCD be a square of side 2a. Find the coordinates of the vertices of this square when A coincides with the origin and AB and AD are along OX and OY respectively.
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Solution
The distance between any two adjacent vertices of a square will always be equal. This distance is nothing but the side of the square.
Here, the side of the square ‘ABCD’ is given to be ‘2a’.
Since it is given that the vertex ‘A’ coincides with the origin we know that the coordinates of this point is (0, 0).
We also understand that the side ‘AB’ is along the x-axis. So, the vertex ‘B’ has got to be at a distance of ‘2a’ from ‘A’.
Hence the vertex ‘B’ has the coordinates (2a, 0).
Also, it is said that the side ‘AD’ is along the y-axis. So, the vertex ‘D’ it has got to be at a distance of ‘2a’ from ‘A’.
Hence the vertex ‘D’ has the coordinates (0, 2a)
Finally, we have vertex ‘C’ at a distance of ‘2a’ both from vertex ‘B’ as well as ‘D’.
Hence the vertex of ‘C’ has the coordinates (2a, 2a)
So, the coordinates of the different vertices of the square are
A(0,0)
B(2a, 0)
C(2a, 2a)
D(0, 2a)
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