The following question i need some help on:

Find the coordinates of the points of intersection of and . Show that the points of intersection are the vertices of a square.

P.S

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- Jan 16th 2010, 10:13 PMPaymemoneyFinding point of intersection
The following question i need some help on:

Find the coordinates of the points of intersection of and . Show that the points of intersection are the vertices of a square.

P.S - Jan 16th 2010, 11:34 PMVonNemo19
- Jan 16th 2010, 11:42 PMbryankek
As you can see and have the same variables, solve it simultaneously and take only real numbers as your solution. To prove that the points are vertices of a square,

i) Multiply the gradient of both the diagonals and show that it is -1.

ii)Find the distance of the diagonals, they should be equal - Jan 17th 2010, 02:12 AMPaymemoney
i have tried to do the following:

using simultaneous equations this is what i have done but it is incorrect:

- Jan 17th 2010, 04:31 AMbryankek
Sorry. but your solution above makes no sense. Anyway here is my solution;

let

be equation (1)

be equation (2)

multiply (1) by 9;

--------(1a)

multiply (2) by 4;

---------(2a)

(1a)-(2a);

substitute and into one of the original equations, in this case (1)

therefore you have

as the solution/coordinates of vertices

and as you can see, they are all equidistant from the origin and that by itself shows that a quadrilateral formed by joining the points would be a square