Median of triangle vertex

Find the equations of the medians of the triangle with the vertex coordinates J(2,5), K(4,-1), and L (-2,-5)
plz and thank you?

 

A median of a triangle is a segment from one vertex to the midpoint of the opposite side.

The first step, then, is to find the midpoints of each side. The easiest way to do this is by using the midpoint formula: (x, y) = (.5(x1 + x2), .5(y1 + y2)). This gives:

Midpoint opposite vertex (2,5): (1,-3)
Midpoint opposite vertex (-2,-5): (3,2)
Midpoint opposite vertex (4,-1): (0,0)

To find the equation of the median, you simply need to find the equation of a line passing through two points: the midpoint and the opposing vertex. Point-slope form is the most convenient: y – y1 = m(x – x1), where m = the slope of the line.

Ie, to find the equation of the line passing through (2,5) and (1,-3), compute the slope to get m = 8. Then, simply plug in the x1 and y1 from one of the two coordinates: y - 5 = 8 (x - 2). You can either leave the equation in this form, or manipulate it in order to get it in terms of y.

Repeat for the two remaining vertex/midpoint pairs.

 

Sins on the right track, let me know if you still need help.