Question

Given the points on the graph below, what are the coordinates of another point that would create a parallelogram?

(6, 3)

(6, 0)

(6, 1)

(6, 2)

Answer 1

A parallelogram has opposite congruent sides and also opposite parallel sides. So, (2,4) - (2,0) is parallel to (6,6) - (x,y) (we don't know it yet). (6,6)-(x,y) is a vertical line segment, and so their x-values will be the same.
(6,6)-(6,y)
The length of (2,0)-(2,4) is also equal to the length of (6,6)-(6,y). The distance between (2,0) and (2,4) is 4 units. So, we could move either up 4 units or down 4 units from (6,6) for our (6,y). So, two points we could use for the last vertex would be (6,6+4) and (6,6-4).
(6,10) or (6,2).

Answer 2

i still dont get it , ughhh...

Answer 3

hmm... something you don't understand, exactly?

Answer 4

yea, i guess all this i try but its not coming to me at all

Answer 5

Basically, we're just using a few properties of parallelograms.
- Opposite sides are congruent/ equal
- Opposite sides are parallel / have same slope

We're looking for a point that will make both of these properties true for our figure.

Answer 6

well i kinda get that part, guess i'll be studying more on this lesson then

Answer 7

You probably just need to grab some graph paper to visually observe where the points are and where the missing point should go.

Answer 8

well idk the picture is there and everything

Answer 9

I see, well, let me help you out..

Answer 10

ok

Answer 11

@Hero --> Would you post the graph for the other point derived by AccessDenied?
Thanks.
(6,10) or (6,2)

Answer 12

there's actually another point that also makes a parallelogram, except that one and (6,10) aren't on the graph provided. We could find it in a similar fashion to finding the others, only we'll be using the slope of a nonvertical/nonhorizontal line

I graphed all three parallelograms that are made on one graph here, hopefully its not too messy.

Answer 13

Thanks for graphing these.
I have spatial viewing difficulties. I can see two of the parallelograms but not the third because I was following the colors of the sides of the parallelograms. When some of the segments coincided, the colors changed, and for me, the entire set of graphs flipped out into a 3-D optical illusion. I'll just need to graph them separately. If you don't mind saying, where are you doing these graphs?

Answer 14

i just used paint + some graph paper from online.

Answer 15

hopefully this turns out well, im uploading the same file twice but saved different times

Answer 16

aww, it turned out the same... well, there's the second one two times

Answer 17

@AccessDenied --> Thanks for your time and effort. After viewing the graphs individually, I am able to see them collectively.

Answer 18

@AccessDenied , your efforts to help @JahEmpress in this case may only confuse her further.

Answer 19

yep your right

Answer 20

well, i'll attempt to write up a better explanation later if you're still uncertain.

Answer 21

The answer actually is (6,3).
Why? Because you can clearly tell that the shape forms into a parallelogram.
There. :D