The orthocentre is the intersection of the altitudes of a triangle.
You will need the equation of two of these and find their intersection
Make a sketch:
notice that LN lies on the x-axis, so the altitude from M is simply x = 10
that was too easy.
let's find the altitude to MN
slope of MN = (8-0)/(10-14) = -2
so slope of altitude is 1/2
and passing through (8,0)
0 = (1/2)(8) + b
b = -4
thus y = (1/2)x - 4
but x = 10
then y = (1/2)(10) - 4 = 1
the orthocentre is (10,1)
As an additional check, find the remaining altitude and verify by subbing in (10,1)
Find the coordinates of the orthocenter of the triangle with the given vertices.
L (8,0) M (10,8) N (14,0)
1 answer
1 answer