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Parllelogram - Coordintes

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by pradeepspanchal » Thu Dec 09, 2010 2:33 am
ABCD is a parallelogram in the xy- rectangular coordinate plane, three of the four vertices of this parallelogram are (5,15),(5,25), and (-5,15).Which of the following can be the coordinates of the fourth vertex?

a. (-5,-5)
b. (15,25)
c. NA
d. NA
e. NA

I check dramatically both produce an parallelogram . Please help to streamline the answer.

Thanks in advance
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by Night reader » Thu Dec 09, 2010 2:40 am
pradeepspanchal wrote:ABCD is a parallelogram in the xy- rectangular coordinate plane, three of the four vertices of this parallelogram are (5,15),(5,25), and (-5,15).Which of the following can be the coordinates of the fourth vertex?

a. (-5,-5)
b. (15,25)
c. NA
d. NA
e. NA

I check dramatically both produce an parallelogram . Please help to streamline the answer.

Thanks in advance
I end up with (-5,10) => the sides must be parallel in parallelogram ...
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by Rahul@gurome » Thu Dec 09, 2010 3:58 am
pradeepspanchal wrote:ABCD is a parallelogram in the xy- rectangular coordinate plane, three of the four vertices of this parallelogram are (5,15),(5,25), and (-5,15).Which of the following can be the coordinates of the fourth vertex?

a. (-5,-5)
b. (15,25)
c. NA
d. NA
e. NA

I check dramatically both produce an parallelogram . Please help to streamline the answer.
The clues to the solution are:
  • 1. The opposite sides must be parallel.
    2. Length of the opposite sides must be same.
Keep this clues in mind and draw the figure accordingly, you'll get it.

Image

Refer to the above image.
Black points are given. Possible third vertexes are Red, Blue and Green points.
Only the coordinate of red point is in the option.

Correct answer is B.
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by pradeepspanchal » Thu Dec 09, 2010 4:46 am
Thanks Rahul , the diagram gives good clarity

I find the mistake missed the equality of length!
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by diebeatsthegmat » Fri Dec 10, 2010 6:14 am
Rahul@gurome wrote:
pradeepspanchal wrote:ABCD is a parallelogram in the xy- rectangular coordinate plane, three of the four vertices of this parallelogram are (5,15),(5,25), and (-5,15).Which of the following can be the coordinates of the fourth vertex?

a. (-5,-5)
b. (15,25)
c. NA
d. NA
e. NA

I check dramatically both produce an parallelogram . Please help to streamline the answer.
The clues to the solution are:
  • 1. The opposite sides must be parallel.
    2. Length of the opposite sides must be same.
Keep this clues in mind and draw the figure accordingly, you'll get it.

Image

Refer to the above image.
Black points are given. Possible third vertexes are Red, Blue and Green points.
Only the coordinate of red point is in the option.

Correct answer is B.
why the correct answer is not A???
if i draw the four vertexes, i will also get a parallelogram with the same equal and opposite sides :(
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by Rahul@gurome » Fri Dec 10, 2010 11:51 am
diebeatsthegmat wrote:why the correct answer is not A???
if i draw the four vertexes, i will also get a parallelogram with the same equal and opposite sides :(
Refer to this image:
Image
The above image is drawn to scale where length of the each small square is taken as 5 units. The black points (A, b and C) are the given three points whereas the red one (D) is the point with coordinate (-5, -5). Clearly ABCD is not a parallelogram. To be more precise: Neither AB and CD is parallel nor they are of same length; AD and BC are parallel but they are not of same length.
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by diebeatsthegmat » Fri Dec 10, 2010 5:48 pm
Rahul@gurome wrote:
diebeatsthegmat wrote:why the correct answer is not A???
if i draw the four vertexes, i will also get a parallelogram with the same equal and opposite sides :(
Refer to this image:
Image
The above image is drawn to scale where length of the each small square is taken as 5 units. The black points (A, b and C) are the given three points whereas the red one (D) is the point with coordinate (-5, -5). Clearly ABCD is not a parallelogram. To be more precise: Neither AB and CD is parallel nor they are of same length; AD and BC are parallel but they are not of same length.
ohh yeah, i misread it (-5,5) . my bad, sorry....
thanks
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