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Mathematics 8 Online
OpenStudy (anonymous):

HELP PLEASEEE!

OpenStudy (anonymous):

OpenStudy (anonymous):

Let's graph these points and connect them to get a visual of what we're dealing with here:

OpenStudy (here_to_help15):

Were in the same school :P Let me see if i can help.

OpenStudy (anonymous):

I'm not the best at questions like this, here_to_help15 should be able to help you finish this. Use the graph if it helps. :)

OpenStudy (aum):

Nice diagram. It would be helpful if the coordinates of each point is included in the diagram.

OpenStudy (anonymous):

@Here_to_Help15 since we are in the same school you know that this is a workpad question and i have to show all of the work to get all 5 points..

OpenStudy (here_to_help15):

Oh right lets see.

OpenStudy (aum):

First plot the 4 points so you know how they are oriented. Then find the slopes of opposite sides and prove they are parallel which would make it a parallelogram. Then find the slopes of the diagonals and prove they are perpendicular. That is, the product of their slopes = -1. That will make it a rhombus.

OpenStudy (here_to_help15):

I hate those questions but lemme see if i could be any help.

OpenStudy (here_to_help15):

Do you think you did good with the other questions before this question?

OpenStudy (here_to_help15):

This should be the last 1 or are there a couple of them?

OpenStudy (anonymous):

this is the last one

OpenStudy (aum):

A (-5,-1); B(-9, 6); C (-1, 5); D (3, -2) What is the slope of the line AB? Slope = \(\Large \frac{y_2-y_1}{x_2-x_1}\)

OpenStudy (here_to_help15):

Sorry Reilly couldn't help:(

OpenStudy (aum):

I can walk you through this question if you do the calculation part.

OpenStudy (anonymous):

\[\frac{ -7 }{ 4 }\]

OpenStudy (aum):

Good. What is the slope of the line CD?

OpenStudy (anonymous):

\[\frac{ -7 }{ 4 }\]

OpenStudy (aum):

Good. Slope of AB = Slope of CD = -7/4 Since their slopes are the same, AB and CD are parallel.

OpenStudy (aum):

Find slope of AD. Find slope of BC.

OpenStudy (anonymous):

okay thank you!!!

OpenStudy (anonymous):

\[\frac{ -1 }{ 8 }\]

OpenStudy (anonymous):

for ad?

OpenStudy (aum):

Correct.

OpenStudy (anonymous):

\[\frac{ -1 }{ 8 }\]

OpenStudy (anonymous):

for bc

OpenStudy (aum):

Correct. Slope of AD = Slope of BC = -1/8 Since their slopes are the same, AD and BC are parallel. Earlier you proved AB and CD are parallel. Since the opposite sides are parallel, this figure is a parallelogram. Find the slope of AC. Find the slope of BD.

OpenStudy (anonymous):

ac= \[\frac{ 6 }{ 4 }\]

OpenStudy (aum):

Yes, but simplify it to 3/2.

OpenStudy (anonymous):

BD= \[\frac{ -8 }{ 12 }\]

OpenStudy (anonymous):

ohh okay

OpenStudy (aum):

Yes, but simplify it to -2/3

OpenStudy (anonymous):

okay!

OpenStudy (aum):

Slope of AC = 3/2 Slope of BD = -2/3 (Slope of AC) x (Slope of BD) = 3/2 x (-2/3) = -1. If the product of the slopes is -1, the lines are perpendicular. Therefore, AC and BD are perpendicular. So the diagram is a parallelogram with perpendicular diagonals. Therefore, the figure is a rhombus.

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