Question

Three consecutive vertices of a parallelogram are (-2, -1), (1, 0) and (4, 3). Find the coordinates of the fourth vertex.

Answer 1

Diagonals of a parallelogram bisect each other,
let the point of intersection of diagonals be P(m,n)

m = (-2+4)/2 = 1
n = (-1+3)/2 = 1

Let the fourth vertex of a parallelogram be (x,y)

m = (1+x)/2
1 = (1+x)/2
x = 1

n = (0+y)/2
1 = (0+y)/2
y = 2
____________________
Hence the fourth vertex is (1,2)

Answer 2

A (-2,-1) = (x1 , y1)
B (1,0) = (x2,y2)
C(4,3) = (x3,y3)

We have to find D(x4,y4)

To find x4,
(x1 + x3) = ( x2+x4)
-2 + 4 = 1 + x4
2 -1 = x4
x4 = 1

To find y4,
y1 + y3 = y2 + y4
-1 + 3 = 0 + y4
x4 = 2

So the 4th vertex = (1,2)