# Thread: Vertices of a parallelogram?

1. ## Vertices of a parallelogram?

Goodness I don't understand this at all!!! I understand finding the coordinates of a parallelogram, but this makes no sense.

So it says "Which of the set of points cannot be the vertices of parallelogram ABCD?"

options are

a) A (-4, -2), B (2, 0), C (3, 3), D (-2, -1)

b) A (-2, -1), B (3, -2), C (4, 1), D (-1, 2)

c) A (0, -2), B (4, -1), C (5, 2), D (0, 5)

d) A (0, -2), B (5, -3), C (7, 1), D (2, 2)

so can someone tell me what formula to use to find the answer? (I'm assuming there's a formula!)

2. Originally Posted by oXCryssieLeahXo
...

So it says "Which of the set of points cannot be the vertices of parallelogram ABCD?"

options are

a) A (-4, -2), B (2, 0), C (3, 3), D (-2, -1)

b) A (-2, -1), B (3, -2), C (4, 1), D (-1, 2)

c) A (0, -2), B (4, -1), C (5, 2), D (0, 5)

d) A (0, -2), B (5, -3), C (7, 1), D (2, 2)

...
The properties of a parallelogram are:

1. The diagonals have a common midpoint.
2. 2 pairs of parallel sides
3. The parallel sides have the same length (#3 is equivalent to #2)

First check if
$\displaystyle M_{AC} = M_{BD}$

So only b) and d) could be a parallelogram

Check if

$\displaystyle (\overline{AB})\ \parallel \ (\overline{CD})$

only d) is left. Since $\displaystyle \left(\begin{array}{c}-5\\1\end{array}\right) = k \cdot \left(\begin{array}{c}5\\-1\end{array}\right)$ the sides $\displaystyle (\overline{AB})\ \parallel \ (\overline{CD})$

PS: Fröhliche Ostern!

3. ## Thank yah

Originally Posted by earboth
The properties of a parallelogram are:

1. The diagonals have a common midpoint.
2. 2 pairs of parallel sides
3. The parallel sides have the same length (#3 is equivalent to #2)

First check if
$\displaystyle M_{AC} = M_{BD}$

So only b) and d) could be a parallelogram

Check if

$\displaystyle (\overline{AB})\ \parallel \ (\overline{CD})$

only d) is left. Since $\displaystyle \left(\begin{array}{c}-5\\1\end{array}\right) = k \cdot \left(\begin{array}{c}5\\-1\end{array}\right)$ the sides $\displaystyle (\overline{AB})\ \parallel \ (\overline{CD})$

PS: Fröhliche Ostern!

wow thank you SO much. Makes sense. I kinda feel dumb now that I didn't figure that out myself!!

Frohe Ostern an dir auchh! =]]

4. Hello, oXCryssieLeahXo!

I don't suppose you tried to PLOT the points . . .

Which of the set of points cannot be the vertices of parallelogram ABCD?

. . $\displaystyle a)\;A (\text{-}4, \text{-}2),\;B (2, 0),\;C (3, 3), D\;(\text{-}2, \text{-}1)$
Code:
                            |           C
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.   .   .   .   .   +   .   .   .   .
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- + - + - + - + - + - + - + - o - + - + -
D       |       B
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A               |
No, I don't think so . . .

### in discrete Mathematics vertices of parallelogram formula

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