



 
Hi Katie, Let's look at b). A median of a triangle joins a vertex to the midpoint of the opposite side. In my diagram B has coordinates (a,0), C has coordinates (a, 0) and A has coordinates (b,c). O is the origin which is the midpoint of BC and M is the midpoint of AB. M has coordinates ((b  a)/2, c/2). The median from A to O has equation
and the median from C to M has equation which simplifies to To find the coordinates of the intersection of the medians AO and CM solve the two equations. Setting the ycoordinates equal gives the equation Solving for x I found x = b/3. Then I substituted x = b/3 into the equation for the median AO and found y = c/3. Thus the medians intersect at (b/3, c/3). I hope this helps,
 


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