SOLUTION: The vertices of △ABC are A(4, 4), B(-6, 2), and C(2, 0). Find an equation in slope y-intercept form for the median from vertex A.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The vertices of △ABC are A(4, 4), B(-6, 2), and C(2, 0). Find an equation in slope y-intercept form for the median from vertex A.      Log On


   

Question 1208624: The vertices of △ABC are A(4, 4), B(-6, 2), and C(2, 0). Find an equation in slope y-intercept form for the median from vertex A.
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

Answer: y+=+expr%281%2F2%29x+%2B+2

Explanation

Let D be the midpoint of segment BC.
Use the midpoint formula, or follow a process similar to this question, to find that D = (-2,1)

The equation we want to find is through A(4,4) and D(-2,1)
Let's find the slope of this line.




m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29

m+=+%281+-+4%29%2F%28-2+-+4%29

m+=+%28-3%29%2F%28-6%29

m+=+1%2F2
The slope of line AD is 1/2


Now apply point-slope form and solve for y.
y-y%5B1%5D+=+m%28x+-+x%5B1%5D%29

y-y%5B1%5D+=+expr%281%2F2%29%28x+-+x%5B1%5D%29 Plug in the slope

y-4+=+expr%281%2F2%29%28x+-+4%29 Plug in the coordinates of point A (you could also use the coordinates of point D)

y-4+=+expr%281%2F2%29x+-+2

y-4+=+expr%281%2F2%29x+-+2%2B4

y+=+expr%281%2F2%29x+%2B+2
This equation has slope 1/2 and y intercept 2.


The equation of the line y+=+expr%281%2F2%29x+%2B+2 is in blue.

You can use a tool like GeoGebra to verify the answer. Desmos is also a good choice.