Question

If A(1,2),B(4,3) and C(6,6) are the three vertices of a parallelogram ABCD, find the coordinates of fourth vertex D.

Answer 1

Place the points in a graph paper with respect to OX and OY rectangular axes and you will see that the vertex D has coordinates (3,5).

Hope this helps you.

Answer 2

AC = BD
They will have the same midpt. (Since, in a parallelogram diagonals bisect each other)

Now, To find the midpt we will use midpoint  formula for AC.

Let the point E(x,y).
E(x,y) = [x₂+x₁/2 , y₂+y₁/2]
= 6+1/2 , 6+2/2
= [7/2 , 4]
The midpoint of AC and BD is [7/2 , 4]

Now,
E(7/2,4) = [x₂+x₁/2 , y₂+y₁/2]
= [x+4/2 , y+3/2]

For x,

x+4/2 = 7/2
x + 4 = 7
x = 3

For y,

y+3/2 = 4
y+3 = 8
y = 5

Hence the coordinates of the fourth vertex is [3,5].