Question

Points A(3,1),B(5,1),C(a,b)D(4,3) are the vertices of parallelogram ABCD.find the values of a,b

Answer 1

This sum can be done by the help of diagonal

Answer 2

Given:

The coordinates of three sides of a parallelogram, to find the coordinates of unknown sides of a parallelogram represented by a, b.

Answer:

a=6.

b=3.

Step-by-step explanation:

In a parallelogram the opposite sides should be parallel.

In parallelogram ABCD AB should be parallel to CD

and AD should be parallel to BC.

The slope of the sides should be equal

slope of AB= 0, that is parallel to x axis

since slope of CD=AB

which implies slope of CD=0;

therefore 3-b÷4-a=0;

            3-b=0

            b=3.

Similarly slope of BC=Slope of AD

slope of BC=b-1÷a-5

                   =3-1÷a-5

                   =2÷a-5.

slope of AD=3-1÷4-3

                   =2

2÷a-5=2

a=6.

Therefore the unknown values are a=6, b=3.