Plz help me

2009-04-10 8:51 am
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1:

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?

回答 (2)

2009-04-16 5:19 am
✔ 最佳答案
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)


2009-04-10 9:55 am
(a) -7

(b) 6

(c) 8

(You can draw diagram by freeware)


收錄日期: 2021-04-25 22:42:56
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20090410000051KK00097

檢視 Wayback Machine 備份