Question

For parallelogram ABCD, A(0, 0), B(a, b), and D(c, 0) are three of its vertices. Find the coordinates of C in terms of a, b, c.

(c, b)

(a + c, b)

(a, b + c)

Answer 1

Since AD is parallel to BC then the distance in the y direction between the two segments must be the same.

Since you are given this distance in the B coordinates as b, the second coordinate for C must also be b. So you now know this much: C coordinates are (?,b).

Now you need to find the first coordinate for C.

Since AB is parallel to DC, then the distance in the x direction must be the same.

Since you are given this distance in the D coordinates as c, the first coordinate for C must be this distance plus distance for the first coordinate in B.

So the first coordinate for C is a+c.

So the two coordinates for C are (a+c, b)