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coordinate geometry

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coordinate geometry

by rattan123 » Mon Dec 26, 2011 6:00 am
The mid points of a triangle are (x1,y1), (x2,y2), (x3,y3).find the vertices of the triangle?
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by Anurag@Gurome » Mon Dec 26, 2011 6:29 am
rattan123 wrote:The mid points of a triangle are (x1,y1), (x2,y2), (x3,y3).find the vertices of the triangle?
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p + r = 2x1...Equation 1
r + t = 2x2...Equation 2
p + t = 2x3...Equation 3
q + s = 2y1...Equation 4
s + u = 2y2...Equation 5
q + u = 2y3...Equation 6

Eqn 1 - Eqn 2 gives
p - t = 2(x1 - x2), now adding this equation to equation 3,
2p = 2x3 + 2(x1 - x2)
p = x3 + x1 - x2
x3 + (x1 - x2) - t = 2(x1 - x2)
t = x3 - x1 + x2

Similarly we can find the other coordinates. Hope that helps.
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by rattan123 » Mon Dec 26, 2011 6:31 am
thnx...this came as a question...this means i have done it correctly..
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by ronnie1985 » Mon Dec 26, 2011 8:42 pm
If (a1,b1) (a2,b2) (a3,b3) are the vertices, then a1+a2 = 2x1,b1+b2 = 2y1 and similarly other equations can be formed and then after solving we will get:-
a1 = 2x2
a2 = 2x3
a3 = 2x1
b1 = 2y2
b2 = 2y3
b3 = 2y1
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by Anurag@Gurome » Mon Dec 26, 2011 8:44 pm
rattan123 wrote:thnx...this came as a question...this means i have done it correctly..
You are welcome!
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