Question

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

Answer 1

Answer:

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})(

2

7+8

,

2

3+2

)=(

2

15

,

2

5

)

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

2

6+9

,

2

1+4

)=(

2

15

,

2

5

)

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.