Question

Given parallelogram ABCD with vertices A(0,6), B(4,9), C(10,6), what are the coordinates of vertex D?

a) D(6,3)
b) D(14,3)
c) D(14,6)
d) D(6,9)

Answer 1

The coordinates of vertex D in parallelogram ABCD are (14, 9) found through vector addition, taking into account the parallel sides of the parallelogram. The correct option is c.

Step-by-step explanation:

The coordinates of vertex D in the parallelogram ABCD can be found using the properties of parallelograms. Since AB is parallel to CD and BC is parallel to AD, you can find the coordinates of D by vector addition. The coordinates of point B relative to point A (the vector AB) are (4, 9) - (0, 6) = (4, 3).

Since CD is parallel and equal in length to AB, the vector CD will also be (4, 3). By adding this vector to point C (10, 6), you'll find the coordinates of point D. Therefore, D = C + CD = (10, 6) + (4, 3) = (10+4, 6+3) = (14, 9). The correct option is c.