Question

In the coordinate plane, three vertices of rectangle PQRS are P (0, 0), Q (0, b), and S (c, 0). What are the coordinates of point R?

Answer 1

Co-ordinates of R must be (c,b).

Explanation:

We are given a rectangle PQRS with the co-ordinates P(0,0), Q(0,b) and S(c,0).

It is required to find the co-ordinates of R(x,y).

Since, we know that,

The possible line segments in the rectangle PQRS are PQ, QR, RS and SP.

This means that, the point P is connected to Q, which is connected to R, which is further connected to S and S finally meets the point P.

Since, the point Q is connected to R by the straight line y= b and the point S is connected to R by the straight line x= c.

As, R is the point where these two lines meet as shown in the figure.

We get, the co-ordinates of R must be (c,b).

Answer 2

R(c,b)

Explanation:

Polygons are always named in either clockwise or in the counter-clockwise order. In the rectangle PQRS, the order is clockwise as the rectangle have four right angles and since the coordinate P of the given rectangle starts from the origin that is (0,0), then the second point that is Q is straight up the Y axis that is (0,b) and S(c,0) is straight along the x axis, the point R must be over the same distance as S=c, and up the same distance as Q=b which means that R must be at (c,b). Therefore, the coordinates of point R is (c,b).