Question

if (30), (5,2) and (-2,-6) on the vertices
d a parallelogram taken in order, find the
fourth vertex​

Answer 1

Answer:

D(3,2)

Sol. Let A(1,−2), B(3,6) and C(5,10) be the three vertices of a parallelogram ABCD and let its fourth vertex be D(a,b).

Join AC and BD. Let AC and BD intersect at point O.

We know that the diagonals of a parallelogram bisect each other.

So, O is the midpoint of AC as well as that of BD.

Using Midpoint formula X=(

2

x

1

+x

2

)and Y=(

2

y

1

+y

2

)

A(1,−2)≡(x

1

,y

1

), C(5,10)≡(x

2

,y

2

)

Midpoint of AC is (

2

1+5

,

2

−2+10

), i.e.,(3,4)

Midpoint of BD is (

2

3+a

,

2

6+b

)

∴

2

3+a

=3 and

2

6+b

=4

3+a=6 and 6+b=8

a=3 and b=2

Hence, the fourth vertex is D(3,2).

hope it helps you.

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