maths

Orthocentre of a triangle is the point of intersection of the threealtitude of the triangle.

Let OP, AQ and BR be the three altitude of ΔOAB.

Slope of AB = (24 + 24)/(18 - 18) = 48/0
Slope of OP = 0
OP passes through O(0, 0) with slope 0.
Hence, equation of OP :
(y - 0)/(x - 0) = 0
OP: y = 0 ...... [i]

Slope of OB = (24 - 0)/(18 - 0) = 4/3
Slope of AQ = -1/(4/3) = -3/4
AQ passes through A(18, -24) with slope -3/4.
Hence, equation of AQ :
(y + 24) / (x - 18) = -3/4
4y + 96 = -3x + 54
AQ: 3x + 4y + 42 = 0 ...... [ii]

Put [i] into [ii] :
3x + 4*0 + 42 = 0
x = -14

Hence, the x-coordinate of the orthocenter = -14

2012-01-25 01:02:34 補充：
To ☂雨後陽光☀ :

The point of intersection of the three perpendicular bisectors of a triangle is called the circumcenter of the triangle, but NOT the orthocenter.