1)Given two points A(-6,17) and B(3,-1), find the coordinate of a point which divides AB internally in the ratio
(a) 2:1(i.e.AP:PB=2:1),
(b)4:5
2)In the figure, the line segment AB cuts the x-axis and the y-axis at P and Q respectively. Find
(a) the ratios AP:PB and AQ:QB
(b) the soordinate of the mid-point M of PQ.
figure:http://postimg.org/image/cnp0lmum1/
Need steps,plz!
F3 Maths Problems
2015-02-16 6:32 am
回答 (1)
2015-02-17 3:57 pm
✔ 最佳答案
(1) (a) Let P be (x,y)x = [(-6)(1) + (3)(2)]/(1 + 2) = 0/3 = 0
y = [(17(1) + (-1)(2)]/(1 + 2) = 15/3 = 5. P is (0,5)
(b)
x = [(-6)(5) + 3(4)]/(4 + 5) = - 18/9 = - 2
y = [17(5) + (-1)(4)]/(4 + 5) = 81/9 = 9. P is (-2, 9).
(2)
(a) The y - coordinate of P is zero. Let AP : PB = r : s. So
0 = [(-6)(s) + 15(r)]/(r + s)
0 = - 6s + 15r
6s = 15r
r/s = r : s = 6/15 = 2/5 = 2 : 5 = AP : PB.
The x - coordinate of Q is zero. Let AQ : QB = r : s. So
0 = [(-16)s + 12r]/(r + s)
16s = 12r
r/s = 16/12 = 4/3. So AQ : QB = 4 : 3.
(b)
Let P be (x, 0).
Slope of PA = slope of AB
(-6 - 0)/(-16 - x) = [15 - (-6)]/[12 - (-16)]
- 6/(-16 - x) = 21/28
6/(16 + x) = 3/4
2/(16 + x) = 1/4
8 = 16 + x
x = 8 - 16 = -8. P is (- 8,0)
Let Q be (0, y)
Slope of AQ = slope of AB
[y - (-6)]/(0 - (-16)] = 3/4
(y + 6)/16 = 3/4
(y + 6)/4 = 3
y + 6 = 12
y = 12 - 6 = 6. Q is (0,6)
So the mid- point of PQ, M is [ (-8 + 0)/2, (0 + 6)/2] = (- 4, 3).
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