These ordered pairs represent 3 vertices of a parallelogram: (0,1);(3,1);(1,3). ?

Question

What is the ordered pair of the 4th vertex?

A.) (0,3)

B.) (3,3)

C. (-2,3)

D. (3,-1)

Please explain how you got the answer. Thanks.

Answer 1

We make a sketch and see that (of course),

the three points form a triangle. (Black)

See this figure: http://i33.tinypic.com/ae79qv.jpg

There are 3 possible points which complete a parallelogram,

depending on which two sides of the triangle we use.

The points (0,1) and (3,1) make a horizontal line.

(Blue)

We could consider that line to be one of the diagonals

of the parallelogram, and then the fourth point is

over -1 and down 2 from (3,1) which would be (2,-1).

That is not one of the choices, so that horizontal line

must be one of the sides.

(Green)

If the parallel side goes to the right from (1,3), then

the fourth point is over +3 from (1,3) which would be to (4,3).

That is not one of the choices, so we continue.

(Red)

If we make a horizontal line to the left of (1,3), it goes

to (-2,3) which is choice C and that appears to be the

desired answer.

.