Quandaries and Queries


hey my name is maria..im a student in university...please answer my question as soon as possible...

Q1)find x and y
i solved it using substitution and the answers were (2,1)

Q2)are these 3 lines concurrent?
i replaced the values of x and y in the third equation and found out that they are not concurrent, because they are not equal.

Q3)find the coordinates of the centroid of triangle ABC
i want your help here to solve the 3rd question i got stuck..

thnx for helping me out



Hi Maria,

I am assuming that ABC is the triangle formed by the lines L1, L2 and L3.

From your calculations the point of intersection of L1 and L2 is (2,1). I am going to call this point A. Now solve L1 and L3 to find where they intersect and call that point B. Finally solve L2 and L3 to find their intersection and call this point C. Thus you have the vertices of the triangle.

Suppose that you have a triangle with vertices (a1, b1), (a2, b2) and (a3, b3). The centroid of this triangle has x-coordinate

 (a1 + a2 + a3)/3

and y-coordinate

 (b1 + b2 + b3)/3



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