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Please explain the questions clearly.1. Let O be the origin. If the coordinates of points A and B are (48, 0) and (24,18) respectively, then the y-coordinate of the a) circumcentre of triangle ABO isb) centroid of triangle ABO isc) in-centre of triangle OAB isIf you can answer with a diagram,... 顯示更多 Please explain the questions clearly. 1. Let O be the origin. If the coordinates of points A and B are (48, 0) and (24,18) respectively, then the y-coordinate of the a) circumcentre of triangle ABO is b) centroid of triangle ABO is c) in-centre of triangle OAB is If you can answer with a diagram, that's the best! 更新: Steps?? 更新 2: I have the answer, but I don't know the steps. 更新 3: 10 points, plz help! I don't want to delete the question. 更新 4: Anyone intends to help?
最佳解答:
From the co-ordinates provided, triangle ABC is an isos. triangle with OB = OA. (a) For circumcentre, it must on the perpendicular bisector of OA, so the x-coordinate must be 24. Let the y-coordinate be y, then distance to origin equals to distance to point B, that is sqrt[(24 -0)^2 + (y -0)^] = (18 -y) 24^2 + y^2 = (18 -y)^2 = 324 + y^2 - 36y 576 - 324 = -36y y = -7, so the circumcentre is (24,-7). (b) For centroid, it is 1/3 above the x - axis, so its y-coordinate is 18/3 = 6. So centroid is (24,6). (c)For in -centre, its y-coordinate is equal to its distance to line OB. Equation of line OB is y = 18x/24 = 3x/4, or 3x - 4y = 0 so distance to line OB = [(24)(3) - 4y]/5 = y (24)(3) = 5y + 4y = 9y y = (24)(3)/9 = 8. So in- centre is (24,8)
其他解答:
(a) -7 (b) 6 (c) 8 (You can draw diagram by freeware)1C924F1C0172E337
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