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

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!! :smile:

Reply 1

Glutamic Acid

17

Are you sure 3y+4x=7 is right equation?

Reply 2

generalebriety

16

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.

Reply 3

NesQuiK.

OP

13

Glutamic Acid

Are you sure 3y+4x=7 is right equation?

yep, confirmed by ans book too :smile:

Reply 4

Glutamic Acid

17

bobson

yep, confirmed by ans book too :smile:

Hmm, I got 3y+2x=7, and both (-1,3) and (5,-1) lie on it, but not on 3y+4x=7.

Reply 5

NesQuiK.

OP

13

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!

Reply 6

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.

Reply 7

Theorist

10

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?

Reply 8

fusionskd

10

Theorist

How can parallel lines intersect?

LOL ditto

Reply 9

Blackwater

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:

:d :d :d

OP

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!

Reply 12

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.

Reply 13

NesQuiK.

OP

13

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.