Question

the three vertices of a parallelogram ABCD,taken in order, are A(1,-2),B(3,6)and C(5,10).find the coordinates of the fourth vertex D.

Answer 1

let A (1,2), B(4,3), C(6,6) are the points given.

Now, let D(x,y) be the fouth vertex

mid point of AC = [1+6/2, 2+6/2]

                       = [7/2,4]

mid point of BD = [x+4/2, y+3/2]

Since the diagonals of the parrallelogram bisect each other

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

x=3                  y=3              By Simplification

Therefore D (3,3)

Answer 2

Answer:

D(3,2)

Step-by-step explanation:

First apply distance formula as AB = DC and BC = AD

From this you will get a equation

x + 3y = 9

And after this apply area formula

to find the area of triangle ABC and ADC areas of both the triangles will be same as the bisector of a parallelogram divides it into 2 congruent triangles

From this you will get a equation

3x - y = 7

By solving both the equations you will get

x = 3

y = 2

Hope it helped you

Please mark it brainliest

Thank you