Question

Use the Slope Formula to determine whether A(5,7), B(1,-2), C(-6, -3), and D(2,5) are the coordinates of the vertices of parallelogram ABCD.

Answer 1

Hi amberlee103 :)

Do you know how parallelogram look like?

Answer 2

there is no diagram

Answer 3

I know there is no diagram. But can you make parallelogram rough sketch?

Answer 4

No. it is a square.This is parallelogram.

Answer 5

Now come to the point. In your question 4 coordinates are given. As I have named the corner of the parallelogram respectively.

Now if you see this diagram. you should noted that two sides are parallel and other two are also parallel.

AB parallel to DC and BC parallel to AD.

Right?

Answer 6

yes

Answer 7

And you should know that parallel lines have same slopes .

Find slopes of AB, BC, CD, DA

So slope of AB must be parallel to slope of DC or CD.

Similarly, slope of BC must be parallel to slope of DA or AD.

Then it will be proved that it is parallelogram.

Answer 8

ok

Answer 9

thats the answer

Answer 10

Yes. But remember condition must be satisfied.

Answer 11

I honestly dont know what Im doing

Answer 12

Its OK. I can help you further just feel free to ask me. :)

Answer 13

Finding slope of AB:
\[\large \text{slope of AB}=\frac{-2-7}{1-5}=\frac{\cancel-9}{\cancel-4}=\frac{9}{4}\]
Similarly find BC, CD and DA.

Can you?
If not then tell me again.