Question

the consecutive vertices of a parrellelogram ABCD are A(1, 2), B(1, 0) and C(4, 0). Find the fourth vertex D. ​

Answer 1

ANSWER

Let M be the midpoint of the diagonals of the parallelograms ABCD.

Co-ordinate of M will be the midpoint of diagonal AC.

Given points are A(1,2),B(1,0) and C(4,0)

Consider line AC

x

1

=1,y

1

=2

x

2

=4,y

2

=0

By midpoint formula, x=(x

1

+x

2

)/2

∴x=(1+4)/2=5/2

By midpoint formula, y=(y

1

+y

2

)/2

∴y=(2+0)/2=2/2=1

Hence the co-ordinates of M are (5/2,1).

M is also the midline of diagonal BD.

Consider line BD and M as midpoint.

x

1

=1,y

1

=0

x=5/2,y=1

By midpoint formula, x=(x

1

+x

2

)/2

∴5/2=(1+x

2

)/2

∴5=1+x

2

∴x

2

=5−1=4

By midpoint formula, y=(y

1

+y

2

)/2

∴1=(0+y

2

)/2

∴1=y

2

/2

⇒y

2

=2

Hence the co-ordinate of D are (4,2).

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