Math Is Fun Forum

Andy910

Guest

Co-ordinate Geometry Rectangle

I'm stuck on this question, I think I'm missing something really obvious. >_<

ABCD is a rectangle, where A, B anc C are the points (3,4), (1,k) and (4,-3) respectively.

i) Find the co-ordinates of the mid point of AC.
ii) Find the gradient of the line AB, giving your answer in terms of k.
iii) Determine the two possible values of k

It is the last one that I am stuck on.

I have found that the midpoint is (3.5,0.5) and that the gradient of the line AB is (4-k)/2. How would you do that last bit? Please help me.

Thanks.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Co-ordinate Geometry Rectangle

I think you should be able to do it if I tell you that two lines at right angles to each other will have gradients that multiply to -1.

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Why did the vector cross the road?
It wanted to be normal.

technique09

Member

Registered: 2008-10-04

Posts: 14

Re: Co-ordinate Geometry Rectangle

The clue mathsyperson gave you was a very useful one, if you were still unable to get the solution, these are the answers i got:

and

k=26/7 and k=30/7 for the other solution.

What might help you is actually drawing the sketch (possibly to understand whats going on a bit better)

Last edited by technique09 (2008-10-09 10:35:39)