Question

M(2, 3), O(3, 0) and N(-1, 1) are the vertices of AMON. If MD is the altitude of Triangle MON, find the equation of MD.​

Answer 1

4x -y = 5

Explanation:

You want the equation of the line through point M(2, 3) that is perpendicular to the line through points O(3, 0) and N(-1, 1).

Perpendicular line

For ∆x = (x2 -x1) and ∆y = (y2 -y1), the equation of the line through (h, k) that is perpendicular to the one through (x1, y1) and (x2, y2) can be written as ...

∆x(x -h) +∆y(y -k) = 0

Application

(∆x, ∆y) = O -N = (3, 0) -(-1, 1) = (3+1, 0 -1) = (4, -1)

Then the line through point (2, 3) is ...

4(x -2) -(y -3) = 0

4x -y = 5 . . . . . . . add 5 to put in standard form

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Additional comment

The altitude is the line through a vertex and perpendicular to the opposite side of the triangle. In the attached, the line MD has the equation 4x -y = 5.