The point where the medians of triangle meet

[honest_denverco09]

EX : A(8, -2) , B(1,5) and C(4, -5) are vertices of triangle ABC.
We knew the equations of the three medians of this triangle are y = -0.36x + 0.9 , y = -1.7x + 6.7 , y = 13x - 57
How can i locate the point where the medians meet ?

Thanks a lot!

[stapel_eliz]

...the equations of the three medians of this triangle are y = -0.36x + 0.9 , y = -1.7x + 6.7 , y = 13x - 57
How can i locate the point where the medians meet ?

The point of intersection of two lines is the solution to the system of equations created by the two lines' equations. So solve the system!

Note: Since the medians all meet at the same place, it doesn't matter which two of the three lines you pick for your system. You'll get the same answer, whatever your choice.

Also, since the three line equations are already solved for "y=", using "substitution" will probably be the simplest method of solution. For instance, if you pick the first two equations, you could "substitute" "-0.36x + 0.9" for "y" in the second equation, getting:

. . . . .-0.36x + 0.9 = -1.7x + 6.7

Then multiply through by 100 to get rid of the decimals:

. . . . .-36x + 90 = -170x + 670

. . . . .134x = 580

...etc, etc, and so forth.

The above assumes, of course, that the equations for the medians are correct. Upon checking, they do not appear to be. It might help if the original exercise and your work so far were posted.

[honest_denverco09]

Thank a lot, you guy! Thankful!