Question

If a vertex of a parallelogram is (2,3) and the diagonals cut at (3,-2), find the opposite vertex.​

Answer 1

We know that by section formula, the co-ordinates of the points which divide internally the line segment joining the points (x

1

,y

1

) and (x

2

,y

2

) in the ratio m:n is

(x,y)=(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

O is the midpoint of AC and BD

∴(2,−5)= mid point of AC

(2,−5)=(

2

x

1

+3

,

2

y

1

+2

)

2

x

1

+3

=2

⇒x

1

+3=4

∴x

1

=1

Also,

2

y

1

+2

=−5

y

1

+2=−10

y

1

=−12

∴c=(1,−12)

(2,−5)= Mid point of BD

(2,−5)=(

2

−1+x

2

,

2

0+y

2

)

⇒

2

−1+x

2

=2

⇒−1+x

2

=4

∴x

2

=5

⇒

2

0+y

2

=−5

∴y

2

=−10

∴D=(5,−10)