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Question
Plot the points P(1, 0), Q(4, 0) and S(1, 3). Find the coordinates of the point R such that PQRS is a square.
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Solution
In point P(1, 0), y-coordinate is zero, so it lies on x-axis.
In point Q(4, 0), y-coordinate is zero so it lies on x-axis.
In point S(1, 3), both coordinates are positive, so it lies in I quadrant.
On plotting these points, we get the following graph.
Now, take a point R on the graph such that PQRS is a square.
Then, all sides will be equal i.e., PQ = QR = RS = PS.
So, abscissa of R should be equal to abscissa of Q i.e., 4 and ordinate of R should be equal to ordinate of S i.e., 3.
Hence, the coordinates of R are (4, 3).
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