標題:
maths
發問:
let o be origin . if the coordinates of a and b are (18,-24)and(18,24)respectively. then the x coordinate of the orthocentre o triangle OAB is???
最佳解答:
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.
maths
發問:
let o be origin . if the coordinates of a and b are (18,-24)and(18,24)respectively. then the x coordinate of the orthocentre o triangle OAB is???
最佳解答:
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.
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