My teacher gave us an answer key to an assignment where we had to find the equation for the altitude, median and perpendicular bisector of a triangle. One of the triangle has vertex coordinates of M(1, 5) N(-4, -4) and O(2, -5). She writes that the slope of the altitude from vertex M to line segment NO is -1/6, while the slope of the perpendicular bisector to NO is -1/4.75. Shouldn't it be the same as the altitude, considering they both meet line NO at right angles?
I sent her an email because she was absent today, and she replied with:
So in the answer key the slope of the perpendicular bisector is calculated by taking the negative reciprocal of the median from vertex M. That has me all kinds of confused, wouldn't that be a line that forms an obtuse/acute angle with side NM? Also, does the fact that the lines of the perp. bisector and the altitude don't originate from the same place have an effect on the slope, considering they form the same angle with the horizontal?Both the altitude and the perpendicular bisector intersect the base of the triangle at a right angle (90 degrees). There are 2 distinct differences between the two:
1)For the equation of the altitude the line is drawn from the vertex (at the top of the triangle), whereas for the perp. bisector it is not drawn from the vertex.
2) The perpendicular bisector intersects the base of the triangle at the midpoint (which is why you use the per. slope of the median). The equation of the altitude does not cut the triangle at the midpoint.
Original answer key is wrong for the given points. Teachers present reply is correct re altitude and per bisector but I dont understand her reference to the median.It has its own equation which has a positive slope.It is formed using point M and the midpoint of NO