Question

If (2,3),(4,6),(-3,5) are three vertices of a parallelogram then fourth vertex is​

Answer 1

Answer:

The fourth vertex should be (-5,2)

Step-by-step explanation:

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Answer 2

Answer:

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=(x1 +x2)/2 and Y=(Y1+y2)/2

A(1,−2)≡(x1,y1 ), C(5,10)≡(x2,y2 )

Midpoint of AC is (1+5/2, −2+10/2), i.e.,(3,4)

Midpoint of BD is (3+a/2,6+b/2)

∴ 3+a/2 =3 and 6+b/2 =4

3+a=6 and 6+b=8

a=3 and b=2

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

Step-by-step explanation:

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