SOLUTION: I'm in grade 10 and I have an assignment that requires me to make a "cheat sheet" that can be used on an upcoming test. The sheet will be marked and I will be able to use it to hel

Question 721473: I'm in grade 10 and I have an assignment that requires me to make a "cheat sheet" that can be used on an upcoming test. The sheet will be marked and I will be able to use it to help me later on. The sheet given has 5 questions that cover all of the material on the test, we have to show the process of how to get the answer.
The question is: "2.What is the difference between an altitude and a median? If you knew the coordinates of the vertices of a triangle, how would you determine the equations of an altitude line and a median line?"
So far I have, "
Median: The line segment joining any vertex of a triangle to the mid-point of its opposite side.
Altitude: The perpendicular drawn from a vertex to the opposite side of the vertex of the triangle."
All I need to know is, using the endpoints, how would you get an equation in y=mx +b form, for an altitude and median line. ( as said in the question above )
Thanks so much,
A grade 10 student.

Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
ALTITUDE
You know the co ordinates of vertices of the triangle.
Suppose BC is the base and AD is the altitude
Find the slope of BC.
The slope of AD will be negative reciprocal of BC.
You know the slope of the altitude and the vertex A
so frame the equation using formula
(y-y1) = m(x-x1)
MEDIAN
By mid point formula find the co ordinates of point where the median touches the base BC.
Again you know the co ordinates of one vertex and the the median point on BC.
frame an equation using two point formula
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