HourglassMage
2. A parallelogram has the vertices (-1, 2), (4, 4), (2, -1) and (-3, -3). Determine what type of parallelogram [10 points]. Find the perimeter and area [20 points].
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HourglassMage
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HourglassMage
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That's what I got...but clearly it's not a parallelogram, so what am I doing wrong, and what do I need to do differently?
HourglassMage
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@ganeshie8, please help!
ganeshie8
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^^thats how it should look.
graphing is a very good idea, but u dont need to graph to solve this problem.
HourglassMage
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Ohhh...duh.
Apparently I'm going to be stupid today, brilliant. Thnx for the help! :)
ganeshie8
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u figured how to work the problem ?
HourglassMage
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BTW, someone told me the answer to this problem was 12. Are they right? I got 4.2...
√((3) – (0))² + ((0) – (3))² = √3² + -3² = √9 + 9 = √18 ≈ 4.2
HourglassMage
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yes, I did
ganeshie8
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show me ur complete work
HourglassMage
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For the first problem?
ganeshie8
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for both
HourglassMage
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Ah...ok
ganeshie8
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what ever u have so far...
HourglassMage
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just a mo, then
HourglassMage
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HourglassMage
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working on the second question now
ganeshie8
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Are you given instructions that u need to work it by graphing ?
HourglassMage
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Yeah, they taught graphing and the distance formula and whatnot
ganeshie8
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no, i mean did the instructions specifically ask u to do this by graphing ?
ganeshie8
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cuz, u should NOT use graphing unless the instructions say so
ganeshie8
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the common/regular way to work this problem is by finding lengths of sides using `distance formula` and the slopes of sides using `slope formula`
HourglassMage
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Those were the directions they gave me
ganeshie8
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cool :) then you're right ! they want u work it by graphing
HourglassMage
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Given that they gave me the graph, I would assume that they want me to solve it by graphing, but I also used the distance formula to find the lengths of the sides
HourglassMage
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ok :)
ganeshie8
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good :)
your length of sides, and perimeter are correct.
but Area is wrong.
ganeshie8
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squaring sides will not give u Area for a rhombus.
HourglassMage
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ohh..just looked it up A - diagonal x diagonal/2
ganeshie8
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Area of rhombus = \(\frac{1}{2} d_1 d_2\)
ganeshie8
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yes^
HourglassMage
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Great, now I have to find the diagonals, lol
ganeshie8
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its easy from graph
ganeshie8
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horizontal diagonal = 3--3 = 6
vertical diagonal = 3--3 = 6
ganeshie8
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So, Area = \(\frac{1}{2} d_1 d_2 = \frac{1}{2} 6*6 = 18\)
ganeshie8
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And that makes the given rhombus a SQUARE !
ganeshie8
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so the given parallelogram is not just a rhombus, its also a SQUARE !
ganeshie8
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for the `type of parallelogram `, you should say that its a `square`
ganeshie8
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if that makes any sense..
HourglassMage
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The parallelogram is a rhombus and a square?
ganeshie8
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just say its a SQUARE !
HourglassMage
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rhomus: all equal sides, two pairs of equal angles
square: equal sides, equal angles
HourglassMage
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oh, ok
HourglassMage
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Does that change my equation for the area, then?
ganeshie8
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all squares are parallelograms
all squares are rhombuses
all squares are rectangles
all squares are quadrilaterals
ganeshie8
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a square is many things
ganeshie8
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yes it will change ur formula, but the answer will be same
HourglassMage
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I see that, lol
ganeshie8
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let me modify it and give u
HourglassMage
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it will be?
HourglassMage
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ok
HourglassMage
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HourglassMage
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how do you find the diagonals inside a rhombus?
ganeshie8
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use the distance formula
HourglassMage
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oh, its the same process, ok, hold on
ganeshie8
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ok, i presume u knw what a diagonal is :)
ganeshie8
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it just connects the opposite vertices
ganeshie8
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|dw:1398867292759:dw|
ganeshie8
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|dw:1398867314860:dw|
ganeshie8
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^^those two line segments joining opposite vertices are diagonals
HourglassMage
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HourglassMage
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Is that correct? I found it odd that I got the same area for #1 and #2...but maybe that's just a coincidence
ganeshie8
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diagonals are not equal in rhombus
ganeshie8
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so u need to calculate the 2nd diagonal also using distance formula
ganeshie8
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and then use the area of rhombus formula :
Area = \(\frac{1}{2}d_1 d_2\)
HourglassMage
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HourglassMage
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@ganeshie8
ganeshie8
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looks good !
HourglassMage
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thnx! :D