1) A straight line L1 : y=mx+c, where m & c are constants, makes an angle of
45degree with the line L2 : x+7y-3=0.
a) Find the two values of m.
b) If the distance from the point(2,0) to L1 is 4 & m>0,
find the two values of c
2)Find the area of the striangle with vertices(1,-2) , (k,k-4) & (k+1,k-1)
in terms of k.
If these points are collinear, find the value of k.
Equations of straight line
2008-05-18 6:23 pm
回答 (1)
2008-05-18 7:12 pm
✔ 最佳答案
1a. tan(π/4) = | (m-(-1/7))/(1+m(-1/7)) | i.e., m=3/4 or -4/3
b. for m>0, i.e., m=3/4,
By the Normal form: | [(3/4)x -y + c]/squr[(3/4)^2+(-1)^2] |=4, for x=2 and y=0
c= 17/10 or c= -47/10
2. Area of triangle = 1/2 [(k-4 +k(k-1)+2(k+1))-(-2(k)+(k+1)(k-4)+(k-1))]
= 6k+3
if they are collinear, area= 0, k=-1/2.
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