Chapter 6.3, Problem 4BCYP

To determine

To determine if the given points are of a parallelogram.

Answer to Problem 4BCYP

It is not a parallelogram.

Explanation of Solution

Given information :

$F(-2,4),G(4,2),H(4,-2),J(-2,-1)$

We know that opposite sides of a parallelogram are equal.

Now we shall use the midpoint formula to determine the mid-point of diagonals FH and GJ.

We know that the diagonals of a parallelogram bisect each other.

Hence if the mid-point of both the diagonals is same than the points are of a parallelogram,

Mid-point of FH is $\left(\frac{-2+4}{2},\frac{4-2}{2}\right)=\left(1,1\right)$

Mid-point of GH is $\left(\frac{4-2}{2},\frac{2-1}{2}\right)=\left(1,\frac{1}{2}\right)$

Hence it is not a parallelogram.