Question

Show that the points A (- 4 - 3) B(3 ,1 )C (3,6 )D (4,2)
taken in the the order form the vertices of a parallelogram

Answer 1

Answer:

The points do not form vertices of a parallelogram

Step-by-step explanation:

The points given can be used to draw a figure using the Cartesian plane

A Cartesian plane has the x axis and the y axis which have both positive integers to the right and negative integers to the left

An appropriate scale is chosen lets say 1 cm to represent a unit

Before drawing you sketch the future that you want to draw them you plot

You finally join the points .

The figure formed is not a parallelogram.

Answer 2

Given,

Four vertices are = A (-4,-3) B(3 ,1 )C (3,6 )D (4,2)

To find,

The given vertices form a parallelogram or not.

Solution,

The four sides of the ABCD polygon will be -

AB,BC,CD,DA

The opposite pair of sides will be -

1) AB and CD ; 2) BC and DA

If ABCD is a parallelogram, then the above mentioned opposite pair of sides will have equal lengths.

Which means, if ABCD is a parallelogram, then

AB = CD

BC = DA

Length of AB = ✓(3+4)²+(1+3)² = ✓49+16 = ✓65 units

Length of BC = ✓(3-3)²+(6-1)² = ✓0+25 = 5 units

Length of CD = ✓(4-3)²+(2-6)² = ✓1+16 = ✓17 units

Length of DA = ✓(4+4)²+(2+3)² = ✓16+25 = ✓41 units

Now, all the four sides of the ABCD is unequal from each other and there are no equal pair of opposite sides. So, ABCD violates the most primary property of being a parallelogram.

Hence, the ABCD is not a parallelogram.