10 points for the first one get the right answer!!!!! please show me how to do it?

Question

find the coordinates of the point of intersection of the medians in the triangle. the triangle have the points: (-a,0) (a,0) (b,c)

Answer 1

The intersection of the medians of a triangle is the centroid.  Since the centroid is at the mean of the coordinates of the three vertices,

((-a + a + b)/3 , (0 + 0 + c)/3) = (b/3, c/3)

alternatively, you could plot two of the medians and find their intersection.  remember that the equation of a line between to points is y-y0=m(x-x0)

(0,0) to (b,c) --> y = (c/b)*x

(-a,0) to ((a+b)/2,(c/2)) --> y = [(c/2) / (a+(a+b)/2)] (x+a)

which simplifies to y = (c*x+a*c)/(b+3*a)

you can solve the system of linear equations to solve for x and y:

(c*x)/b=(c*x+a*c)/(b+3*a) --> x= b/3

y = (c/b)*x --> y = c/3

Answer 2

the answer is:

DO YOUR HOME WORK YOURSELF!