The line joining the points A(-3,5) and B(11,-5) cuts the line L : y = x at the point P and the x-axis at the point Q.
a) Find the coordinates of P and Q.
b) Hence, or otherwise, find the ratios AP : PQ : QB
Rectangle Coordinates System
2008-05-05 5:41 am
回答 (1)
2008-05-05 6:26 am
✔ 最佳答案
a)Eqn. of line AB:
(5 - -5)/(-3 - 11) = (y-5)/(x - -3)
-10/14 = (y-5)/(x + 3)
14(y-5)= -10(x + 3)
14y - 70 = -10x - 30
10x + 14y - 40 = 0
5x + 7y - 20 = 0 -------(1)
Put x=y into (1),
5y + 7y - 20 = 0
12y = 20
y = 5/3
x = y = 5/3
P is (5/3 , 5/3)
Put y=0 into (1),
5x + 7 x 0 - 20 = 0
5x = 20
x = 4
Q is (4 , 0)
b)
AP : PQ : QB
= (5/3 - -3) : (4 - 5/3) : (11 - 4)
= (5/3 + 3) : (4 - 5/3) : (11 - 4)
= 14/3 : 7/3 : 7
= 14 : 7 : 21
收錄日期: 2021-04-14 19:47:49
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