Consider the triangle defined by A=(-2,0) B=(6,0) C=(4,6).

Question

Find equations for the lines that contain the median drawn from B to AC and the median drawn from A to BC. 

Find coordinates for G, the intersection of the medians from A and B.

Let M be the midpoint of AB. determine whether or not M, G, and C are collinear.

Answer 1

You requested: Find equations for the lines that contain the median drawn from B to AC and the median drawn from A to BC. 

 

I think that you meant: Find equations for the lines that contain the median drawn from B to AC and the median drawn from A to BC. 

 

To do this, first find the midpoints of the segments AC and BC, Then equations of those median lines can be written using Point Slope form.

 

Next, you requested: Find coordinates for G, the intersection of the medians from A and B.

To find (x,y) for G, solve the system of linear equations that was developed above.

 

Last request: Let M be the midpoint of AB. determine whether or not M, G, and C are collinear.

One way to determine collinearity of three points is to determine the slope of all lines MG, MC & GC.

If all three of these slopes are the same, then the three points are collinear.