Question

If three consecutive vertices of a parallelogram ABCD are A( 1 , -2 ) ,B ( 3 , 6 ) and C ( 5 , 10 ) , find its fourth vertex D .

Answer 1

hope it will be helpful to you

Answer 2

Answer:

The fourth vertex is (3,2)

Solution:

As given, points A( 1 , -2 ) ,B ( 3 , 6 ) and C ( 5 , 10 )

Let us assume that the vertex of point D is (x, y)

We know diagonal bisects each other,

So mid-point of AC = mid-point of BD……………. ( i )

Now, mid-point of $\mathrm{AC}=\left[\frac{1+5}{2}, \frac{10-2}{2}\right]=(3,4)$

And mid-point of \mathrm{BD}=\frac{3+x}{2}, \frac{6+y}{2}

Hence from equation (i) we can conclude that,

$\frac{3+x}{2}=3$

3+x=6

x=3

$\frac{3+x}{2}=3$

6+y=8

y=2

So vertex of D = (3, 2)