Urgent Questions(7) ^_^

用戶85377

2007-08-15 3:53 am

Show the steps very clearly.
3. The coordinates of A and B are (1,3) and (7,6) respectively. If CA┴AB, Find the coordinates of C?
4. Find the distance between the points A and B.
A(a,1), B(2,a-1), where a>2
5. Which of the following lines are parallel and which of the lines are perpendicular? Why?
AB, BC, CD, AD, BD, AC
6. A=(-7,3), B= (1,9) and AB is the diameter of a circle. Find the coordinates of the centre of the circle and the radius of the circle.

更新1:

Any volunteer helps?

更新2:

I am looking for your help!

更新3:

Attention: Q.5 is cancelled. Because the information is not enough!

更新4:

This part I don't understand. Equation of CA is: (y - 3) = -2 (x - 1) 2x + y - 5 = 0 The coordinates of C can be any pair of solution of the equation above.

更新5:

4. a>2, it can be a negative number.

回答 (1)

用戶82723

2007-08-17 12:02 am

✔ 最佳答案

3. Since CA ⊥AB,
(Slope of AB) (Slope of CA) = -1
(6 - 3) / (7 - 1) x (Slope of CA) = -1
Slope of CA = -2

Equation of CA is:
(y - 3) = -2 (x - 1)
2x + y - 5 = 0

The coordinates of C can be any pair of solution of the equation above.

4. Distance between A and B
= √ [ (a - 2)2 + (a - 1 - 1)2 ]
= √2 (a - 2)

6. Center of the circle = Mid-point of AB
Coordinates of the center of the circle
= ( (1 - 7) / 2 , (9 + 3) / 2 )
= (-3 , 4)

Radius = 1/2 (AB)
= 1/2 x √ [ (9 - 3)2 + (1 + 7)2 ]
= 10

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