S$ Mathe - Ans.fyi 參考答案

S$ Mathe

2012-01-31 9:18 pm

Please to solove the following questions.

1. In each of the following, find the distance between the two given points.
a. A(-8 , -2) and B(-4 , 0)
b. P(2a , -5a) and Q(7a , 7a)
**Leave your answers in surd from if neccessary

2. Prove that the three points D(-5 , -1) , E(-3 , 2) and F(1 , 8) on a
rectangular coordinate plane are collinear.

3. a) express the distance between A(2a , 2a) and B(6a , -a) in terms of a
where a>0.
b) If the distance between A and B is 3 times the distance between
C(0 , 7) and D(-3 , 3), find the value of a.

回答 (1)

用戶2053

2012-01-31 9:43 pm

✔ 最佳答案

1a)AB
= √ ( (- 8 - (-4))² + (- 2 - 0)² )
= √ (16 + 4)
= √ 20
= √ (4 * 5)
= 2√ 5b)PQ
= √ ( (2a - 7a)² + (-5a - 7a)² )
= √ (25a² + 144a²)
= √ (169a²)
= 13a for a ≥ 0 or -13a for a ≤ 0.
2)Only need to show that slope of DE = slope of EF :Slope of DE = (-1 - 2) / ( -5 - (-3) ) = 3/2
Slope of EF = (2 - 8) / (-3 - 1) = 3/2So DEF are collinear.
3)a)AB
= √ ( (2a - 6a)² + (2a - (-a))² )
= √ (16a² + 9a²)
= √ (25a²)
= 5a for a > 0b)AB = 3CD
5a = 3 √ ( (0 - (-3))² + (7 - 3)² )
5a = 3 √ (9 + 16)
5a = 3 * 5
a = 3

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