Question

show that the points A(7,3) B(6,1) C(8,2) D(9,4) taken in order are the vertices of a parallelogram

Answer 1

firstly u have to join AC and BD, then you have to apply diagonal Formula and compare them and prove opposite sides are equal

Answer 2

Given that,

Points A(7,3) B(6,1) C(8,2) D(9,4)

To shows,

The points form the vertices of a parallelogram.

Solution,

We know that the diagonals of a parallelogram bisect each other. It means that we can show that the mid point of AC is equal to the mid point of BD.

We have A(7,3) B(6,1) C(8,2) D(9,4)

The mid point of AC= $(\dfrac{7+8}{2},\dfrac{3+2}{2})=(\dfrac{15}{2}, \dfrac{5}{2})$

The mid point of BD= $(\dfrac{6+9}{2},\dfrac{1+4}{2})=(\dfrac{15}{2}, \dfrac{5}{2})$

It is clear that, Midpoint of AC = Midpoint of BD

So, the points A(7,3) B(6,1) C(8,2) D(9,4) are the vertices of a parallelogram.