f.3 math Coordinate Geometry

2007-10-23 6:38 pm

1Find the coordinates of the midpoint of each line segment
A) S(6,-2) and T(2,2)

B) V(2.9,3.2) and W(3.1, -4.2)

2a).Find the mid-points of the sides of triangleABC whose vertices are A(3,0),B(5,2) and (7,6).

b)Find the centroid of this triangle.

3)For a line segment AB,one endpoint is A(5,1) and the midpoint is M(-1,4).Find the coordinates of endpoint B.

回答 (1)

sing4u1234

2007-10-24 12:25 am

✔ 最佳答案

1A. The x-coordinate of the mid-pt of ST
=(6+2)/2= 4
The y-coordinate of the mid-pt of ST
= (-2+2)/2 = 0
Mid-pt of ST = (4,0)
B. The x-coordinate of the mid-pt of VW
= (2.9 + 3.1)/2 = 3
The y-coordinate of the mid-pt of VW
= (3.2 + (-4.2))/2 = -0.5
Mid-pt of VW = (3, -0.5)
2. (a)Since A=(3,0),B=(5,2) and C=(7,6),
The mid-pt of AB = ((3+5)/2, (0+2)/2) = (4, 1)
The mid-pt of BC = ((5+7)/2, (2+6)/2) = ( 6, 4)
The mid-pt of AC = ((3+7)/2, (0+6)/2) = (5, 3)
(b) The x-coordinate of the centroid
= (3+5+7)/3 = 5
The y-coordinate of the centroid
= (0+2+6)/3 = 2 2/3 ( 2 and 2 thirds, ie 8/3)
The coordinates of the centroid are ( 5, 2 2/3)
3. Let (p,q) be the coordinates of B.
Then, (5+p)/2 = -1
5+p = -2
p = -7
(1+q)/2 = 4
1+q = 8
q = 7
So, the coordinates of B are (-7, 7).

參考: myself

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