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.

Answer 1

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).