parallelogram?

Question

The vertices of a parallelogram are (5,12) (2,7) and (6,1) joined in the order named. Find the 4th vertex.

Answer 1

A(5,12) , B(2,7) , C(6,1) , D(x,y)
Vector AB = Vector DC
Vector AB = (- 3 , - 5)
Vector DC = (6 - x , 1 - y)

6 - x = - 3
x = 9

1 - y = - 5
y = 6

4th Vertex is (9 , 6)

Answer 2

Label the given vertices A, B, C in the order you have given them, and let the fourth one be D.

A is 5 - 2 = 3 units to the right of B, and 12 - 7 = 5 units above B.
D is therefore 3 units to the right of C, and 5 units above C.

That makes the co-ordinates of D (3 + 6, 5 + 1) = (9,6).

Answer 3

A(5,12),B(12,7), C(6,1), D(?,?)
let D be (x,y).
mid point of A&C=(11/2,13/2)
mid point of B&D=(12+x/2,y+7/2)
as the mid point of A&C and B&D are the same
12+x/2=11/2, 12+x=11.....................(1)
y+7/2=13/2, y+7=13................................(2)
x=-1, y=6 answer

Answer 4

In a parallelogram..the opposite sides are always parallel and equal.
plot a graph

from the graph you will notice that the forth vertx will be (9,6)

Answer 5

9,6

My answer is correct. The person below my answer misread one of the vertices. Believe me, than answer is (9,6)