A math (equations of straight lines 25)

[匿名]

2006-12-10 12:21 am

A(6,7) is a point on the line L:3x-y-11=0 and P(1,2) is an given point. Let θ be the acute angle between PA and the line L .
(a) Find tan θ
(b) If B is another point on L such that PA=PB , find the equation of PB
(c) Find the coordinates of B

no need to calculate (a) the answer is 1/2
i just want to know what should i do for (b) & (c) Thx

回答 (1)

The Little Prince of Mathematics

2006-12-10 1:34 am

✔ 最佳答案

(b) Let the equation of PB be y=mx+c,
ABS[(m-3)/1+3m]=1/2
2m-6=-1-3m or 1+3m
m=1(rejected) or m=-7
Sub (1,2) into y=-7x+c,
c=-5.
The equation of PB is y=-7x+9
(c) By solving the two equation,
y=3x+11...............(1)
y=-7x+9................(2)
(1) - (2) : 10x+20=0
x=-2
Sub y into y=3x+11,
y=5.
the coordinates of B are (-2,5).
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alternative way to find (c) directly
(c) Let the coordinates of B is (t, 3t-11),
SQRT[(3t-11-2)^2+(t-1)^2]=SQRT[(7-2)^2+(6-1)^2]
9t^2-78t+169+t^2-2t+1=50
10t^2-80t+120=0
t=6 (rejected) or t=2
Therefore, the coordinates of B is (2, -5).

參考: myself

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