Math Is Fun Forum

franky54

Member

Registered: 2008-11-20

Posts: 3

coordinate geometry question

Hi, I'm hoping someone can help me come up with a formula to determine the rectangular coordinates of the vertex (Xc, Yc) of an isosceles triangle when the coordinates of the two bottom points are known (Xa, Ya and Xb, Yb) and the length of the two equal sides are known (d). I started to work backwards from the distance formula but quickly filled the page with unweildy equations. Assuming that the triangle base is roughly horizontal, I am only interested in the solution that puts the vertex 'above' the base, ie an 'upright' isosceles triangle. TIA for any help. Cheers,

Franky54

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: coordinate geometry question

How much mathematics do you know?  Hopefully vectors are familiar.

You know the vector that goes between the two points in the base of the triangle.  Do you know how to find the vector perpendicular to this one?

Assuming that you do, we know our "top" vertex must lie along this vector (why?).  The only question we have to answer is the length of this vector.  Use Pythagorean theorem for this part.  Once you get the length, call the final vector v, and then your solution is the midpoint between the two known points plus v.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

franky54

Member

Registered: 2008-11-20

Posts: 3

Re: coordinate geometry question

Ricky, thank you, that makes perfect sense to me ... I'm certainly no expert on vectors, but you have given me a direction to go in (no pun intended) and I will look into it further. Hopefully I'll be able to express the vector in terms of a function that can be calculated in a spreadsheet. Cheers,

-franky54

franky54

Member

Registered: 2008-11-20

Posts: 3

Re: coordinate geometry question

Likewise, you've also made me realize that I can easily calculate the coordinates of the midpoint of the base, the distance from a bottom corner to the midpoint, and therefore the lengths of all three sides...I wonder can I now calculate the coordinates of the vertex without invoking vectors..?

-franky54