Question

Help please
Prove or disprove that the quadrilateral defined by the points A(6,4), B(1,3), C(-2,1), D(3,2) is a parallelogram.

Answer 1

@Directrix

Answer 2

http://www.webmath.com/gpoints.html this site helps with graphing points on a coordinate grid.

Answer 3

@TylerMckinney16

At Demos.com , the points were plotted. While the figure may look like a parallelogram, that does not mean it is.

You will need to get the slopes of both pairs of opposite sides of the quadrilateral.

First up:

What is the slope of segment AB.

A has coordinates (6,4)
B has coordinates (1,3)

Answer 4

Go here to calculate the slope:

http://calculator.tutorvista.com/slope-calculator.html

Enter the coordinates of point A and the coordinates of point B.

Click on "calculate slope."

Post what you get for the slope of segment AB.

Answer 5

You should see this after you enter the coordinates.

Answer 6

Ok what next?

Answer 7

This time, you use the online calculator and find the slope of segment CD.

C(-2,1) and D(3,2)

Post what you get.

Answer 8

1.1?

Answer 9

No. Try again.

Answer 10

-0.65625 ? I devided them together and got this.

Answer 11

Use the online calculator.

Enter the coordinates of point C and the coordinates of point D.

Click on "calculate slope."

http://calculator.tutorvista.com/slope-calculator.html

Answer 12

Slope(m)=0.2 and
The Slope-Intercept form is = y=0x+1

Answer 13

Slope of segment AB = .2
Slope of segment CD = .2

If two lines have the same slope, then they are parallel.
We have one pair of parallel lines.

We have to get another pair.

Answer 14

Use the calculator to find the slope of segment BC

B(1,3), C(-2,1)

Answer 15

Oh ok.

Answer 16

Slope(m)=0.667

Answer 17

Find the slope of segment AD:

AD

A(6,4), D(3,2)

Answer 18

Slope(m)=0.667

Answer 19

ok

Answer 20

Slope of segment AB = .2
Slope of segment CD = .2
If the slopes of two lines are the same, then the lines are parallel.
Segment AB is parallel to segment CD
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Slope of segment AD = .667
Slope of segment BC = .667
If the slopes of two lines are the same, then the lines are parallel.
Segment AD is parallel to segment BC.

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If a quadrilateral has both pairs of opposite sides parallel, then the quadrilateral is a parallelogram.
Therefore, Quadrilateral ABCD is a parallelogram.