given three vertices of a rhombus, but how do i find the 4th one?? (c1) Watch

NesQuiK.
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heres the question,

A rhombus has opp vertices at (-1,3) and (5,-1)

a) find the equation of its diagonals, on of the other vertices is (0,-2)

b)find the 4th vertex

so ive got the two equations, 3y+4x=7 and 2y-3x=-4.
now to find the 4th vertex i thought about the midpoint of the first diagoanl, then finding the distance between that and (0,-2), and adding that to get the other vertex, but then i realised that's just silly as i can't get a co-ordinate from that, so if somebody oculd just guide me in the right direction i would be very thankful!!
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Glutamic Acid
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Are you sure 3y+4x=7 is right equation?
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generalebriety
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A rhombus is a parallelogram. That might help. Alternatively, find the distance between (0, -2) and one of the other points, and find the point that's the same distance from both of those other points.
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NesQuiK.
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(Original post by Glutamic Acid)
Are you sure 3y+4x=7 is right equation?
yep, confirmed by ans book too
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Glutamic Acid
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(Original post by bobson)
yep, confirmed by ans book too
Hmm, I got 3y+2x=7, and both (-1,3) and (5,-1) lie on it, but not on 3y+4x=7.
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NesQuiK.
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(Original post by Glutamic Acid)
Hmm, I got 3y+2x=7, and both (-1,3) and (5,-1) lie on it, but not on 3y+4x=7.
oops yeh mistyped it!
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Blackwater
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If you find the equations of the parallel lines using the equations you already have (as parallel lines have the same gradients), you can find the point at which they intersect, which should be the fourth vertex.
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Theorist
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(Original post by Blackwater)
If you find the equations of the parallel lines using the equations you already have (as parallel lines have the same gradients), you can find the point at which they intersect, which should be the fourth vertex.
How can parallel lines intersect?
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fusionskd
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(Original post by Theorist)
How can parallel lines intersect?
LOL ditto
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Blackwater
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You have two lines which aren't parallel to eachother. Each of those has a line in the rhombus that is parallel to it, and these two intersect at the vertex. That's what I'm saying, not that the parallel lines intersect. :p:
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Theorist
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:d :d :d
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NesQuiK.
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urm, well im not a fan of asking for actual solutions, but i just don't undestand these type of questions where you have to find the missing co-ordinates,and i've got my 1st maths progress test on monday, so i could really do with a solution as i can follow it to understand the method....

Greatly appreciate any help, thanks!
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luco123
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You can think of it in terms of vectors:

The vector from vertex (5,-1) to (0,-2) is -5i-1j

Therefore, the vector from (-1,3) to the 4th vertex is the same (-5i-1j) which leaves the answer as (-6,2) I think.
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NesQuiK.
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(Original post by luco123)
You can think of it in terms of vectors:

The vector from vertex (5,-1) to (0,-2) is -5i-1j

Therefore, the vector from (-1,3) to the 4th vertex is the same (-5i-1j) which leaves the answer as (-6,2) I think.
the ans book says (4,4)
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NesQuiK.
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ohhh, i get where (4,4) comes from, thanks for the vector suggestion luco123
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motvivo
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A(-4,-3) B1;-1 c3;4 find D
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Anna vivian
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#17
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A(-4,-3) B1;-1 c3;4 find D
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