Question

If P (1, 2), B (4, 3), X (6, 6) are the three vertices of a Parallelogram PBXC, find the

coordinates of fourth vertex C.

Please help fast please​

Answer 1

Explanation:

Let ABCD be a parallelogram in which the co-ordinates of the vertices are A (1, 2);

B (4, 3) and C (6, 6). We have to find the co-ordinates of the forth vertex.

Let the forth vertex be D ( x , y)

Since ABCD is a parallelogram, the diagonals bisect each other. Therefore the mid-point of the diagonals of the parallelogram will coincide.

Now to find the mid-point P ( x , y) of two points

A(x1,y2) and B(x2,y2) we use section formula as,

P(x,y)=(x1+x22,y1+y22)

The mid-point of the diagonals of the parallelogram will coincide.

So,

Co - ordinate of mid - point of AC = Co -ordinate of mid -point of BD

Therefore,

(1+62,2+62)=(x+42,y+32)

(x+42,y+32)=(72,4)

Now equate the individual terms to get the unknown value. So,

x+42=72

x = 3

Similarly,

y +32=4

y = 5

So the forth vertex is D ( 3 , 5) .