SOLUTION: a triangle, STR ... s=(-4,7) t= (4,7)r=(0,1), and they're asking me to write an equation that contains the median of triangle RST from S to side RT. HELP!!!!!!!!!!!!!!!!!!!!!!!!!

Algebra ->  Length-and-distance -> SOLUTION: a triangle, STR ... s=(-4,7) t= (4,7)r=(0,1), and they're asking me to write an equation that contains the median of triangle RST from S to side RT. HELP!!!!!!!!!!!!!!!!!!!!!!!!!      Log On


   



Question 322502: a triangle, STR ... s=(-4,7) t= (4,7)r=(0,1), and they're asking me to write an equation that contains the median of triangle RST from S to side RT. HELP!!!!!!!!!!!!!!!!!!!!!!!!!
Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!



A median is a line segment drawn from a vertex to the midpoint of
the opposite side. 

So first let's find the midpoint of the side RT, using the
midpoint formula:

midpoint%22%22=%22%22%22%28%22%28x%5B1%5D%2Bx%5B2%5D%29%2F2%22%2C%22%28y%5B1%5D%2By%5B2%5D%29%2F2%22%29%22%22%22=%22%22%22%28%22%280%2B4%29%2F2%22%2C%22%281%2B7%29%2F2%22%29%22%22%22=%22%22%22%28%224%2F2%22%2C%228%2F2%22%29%22%22%22=%22%22%22%28%222%22%2C%224%22%29%22 

Let's call that point M for "Midpoint". So we plot M(2,4):

 

Now we draw the line segment SM, which is the median. I'll draw it
in red:

 

and we want to find the equation of the line that contains that median.

That is, we want to find the equation of the line through the points 
S(-4,7) and M(2,4).  That's the red line:





Use the slope formula: 

m%22%22=%22%22%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29%22%22=%22%22%28%284%29-%287%29%29%2F%28%282%29-%28-4%29%29%22%22=%22%22%28-3%29%2F%282%2B4%29%22%22=%22%22%28-3%29%2F6%22%22=%22%22-1%2F2

Use the point-slope formula:

y-y%5B1%5D%22%22=%22%22m%28x-x%5B1%5D%29

y-7%22%22=%22%22-1%2F2%28x%2B4%29

y-7%22%22=%22%22-1%2F2x%22%22-%22%222%29

y%22%22=%22%22-1%2F2x%22%22%2B%22%225%29

Edwin