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Question

Given points A(4, 3), B(4, -2), C(-4, -1), D(-1, 4). Determine whether quadrilateral ABCD with the given vertices is a parallelogram or not. You must provide work to prove your answer.

Answer 1

i'll help

A parallelogram is a quadrilateral with two sets of parallel sides. The opposite sides of a parallelogram are of equal length.

So AB has to be parallel to CD and AD to BC.

the slope of AB is change in y over change in x, so
(3- -2)/(4-4), since there is a zero in the denoimator it does not exist. by graphing it on an xy axis we can see that it is a straight line.
the slope of CD is -5/3. so therefore the quadrilateral is not a parallelogram

Answer 2

For the indicated quadrilateral to be a parallelogram, the opposite sides must be parallel. If the opposite sides are parallel, then the slopes of the lines must be equal. The slopes of a line is defined as (y2-y1)/(x2-x1). Calculating the slopes m of the four lines we have:

mAB = (3-(-2)/(4-4) = infinite, a vertical line

mBC = (-1 -(-2))/(-4 -4) = -1/8

mCD = (4 - (-1))/(-1 - (-4)) = 5/3

mDA = (3-4)/(4-(-1) = -1/5

None of the slopes are equal, therefore the quadrilateral is not a parallelogram.

[REPOST] Hey, jnice160, what's with the placeholder? It makes it look like you are waiting for a correct answer to show up so you can copy it. Please play fair.

Answer 3

A parallelogram is a quadrilateral whose opposite sides are both parallel and equal in length. Plotting the given points does not reveal a parallelogram; instead, it shows a trapezoid.

Answer 4

Parallelogram definition:
Opposite sides are
* parallel
* equal in length

It's not a parallelogram because DC and AB are not parallel.

slope (DC) = (4-(-1)/ (-1 - (-4) = -5/3
slope (AB) = (-2 - 3) /(4-4) = infinitive => parallel to y-axis

slopes of DC and AB are different, so they're not parallel.

Answer 5

1) Draw a picture
2) Look at picture
3) Examine your head
4) Transform points into 4 vectors
5) Take dot product between connecting vectors
6) Examine dot products, do any of them match
7) If out of 4 dot products there are 2 pairs of 2 matching angles proceed to next step
8) find vector magnitudes
9) do matching magnitudes of vectors match up with matching angles
10) Check head again
11) Now take dot product of non connecting vectors, are they zero
12) Integrate from lower bounds to upper bounds to find area
13) Integrate from left most bounds to right most bounds
14) above numbers should match no matter what, you just did useless work, but if they don't match, take calculus again
15) Once again revert back to picture
16) Observe picture
17) Now that you have stared at the picture for long enough, ask yourself, "Did I pay attention in class where they mentioned the properties of a parallelogram?"
18) Proceed to apologize to community for wasting time with redundant homework questions.
19) Read the math book where problem came from
20) P.S. All of the above is actually a way to prove it is a parallellogram

Answer 6

Vector AB = (0 - 5)
Vector BC = (- 8 1)
Vector CD = (3 5)
Vector DA = (5 - 1)
Vector AB ≠ Vector CD so is not a parallogram.

Answer 7

What?