Question

In the accompanying diagram, three vertices of parallelogram ORST are O(0,0), R(b,d), and T(a,0). What are the coordinates of S?A. (a, b)B. (a+b, d)C. (a+b, b)D. (a, d)

Answer 1

In a parallelogram, the opposite sides are parallel.

This means that RS is parallel to OT. So, the y value of S is the same as the y value of R, which is d, so y = d. Thus:

`S=(x,y)=(x,d)`

Now, we need to find x.

Since the sides RO and ST are also parallel, the x distance from O to R is the same as the x distance from T to S.

The x distance from O to R is

`b-0=b`

The x distance from T to S is

`x-a`

Since these x distances are equal, then:

`\begin{gathered} b=x-a \\ x=a+b \end{gathered}`

Then, the coordinates of S are:

`(a+b,d)`

Which corresponds to option B.