Question

the three vertices of parellogram ABCD, taken in order are A (1,-2) B (3,6) C (5,10) find the coordinate of fourth vertex D

Answer 1

you put this formula in this question i

Answer 2

Answer:

Coordinates of fourth vertex is D(0,-1)

Step-by-step explanation:

Given three of vertices of a parallelogram are A(1,-2), B(3,6), C (5,10).

we have to find the fourth vertex of parallelogram.

Let the coordinates of fourth vertex be D(x, y)

As the diagonals of parallelogram bisect each other

Hence midpoint of BD = midpoint of AC

By mid-point formula

$\text{The coordinates of mid-point of line segment joining the points }(x_1,y_1) and (x_2,y_2) are$

$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Midpoint of BD = Midpoint of AC

$(\frac{1+5}{2},\frac{-2+10}{2})=(\frac{3+x}{2},\frac{6+y}{2})$

⇒ $(3,4)=(\frac{3+x}{2},\frac{6+y}{2})$

Comparing both sides

$3=\frac{3+x}{2}$ and $4=\frac{6+y}{2}$    

gives x=6-3=3     and   y=8-6=2

Hence, coordinates of fourth vertex is D(3,2)