Triangle altitude

Question

an altitude of a triangle is a line segment from a vertex perpendicular to the opposite side. Given the vertices of a triangle to be X (3,2), Y (4,8), Z (6,4) determine the equation of this altitud from the vertex X

Answer 1

The side opposite vertex X is the line YZ, which has a slope of:

 

m = (4-(-8))/(6-4) = -2

 

The altitude for X must be perpendicular to YZ, so it has a slope of -1/m = -1/(-2) = 1/2.  So the equation of the altitude so far is:

 

y = (1/2)x + b

 

Since the altitude passes through X, plug in the coordinates of X, (3.2), to find b:

 

2 = (1/2)*3 + b

3 = 3/2 + b

1/2 = b

 

So the equation of the altitude is:

 

y = (1/2)x + (1/2)