1.in the figure,the straight line L:2X+y-4=0 cuts the x-axis at A and the y-axis atB
a)find the coordinates of A,B
b)if L1 is a straight line passing though A and perpendicular to L,find the equation of L.
c) if L2 is a straight line passing though B and parallel to the x-axis,find the coordinates of the intersection C of L1.and L2
pic:http://i74.photobucket.com/albums/i279/fantasy001x/eba59da4.jpg
math question
2007-09-26 7:10 pm
回答 (2)
2007-09-26 7:20 pm
✔ 最佳答案
As follows~~~圖片參考：http://i182.photobucket.com/albums/x4/A_Hepburn_1990/equation4.jpg?t=1190776833
參考: Myself~~~
2007-09-26 7:31 pm
1) Let B coordinate is (0,y)
A coordinate is (x,0)
Substitue B to L
2(0) + y - 4 = 0
y - 4 = 0
y = 4
Substitue A to L
2x + 0 - 4 = 0
2x = 4
x = 2
therefore B (0,4) and A (2,0)
b) Firstly, find the slope of L
Let m is the slope of L
2x + y - 4 = 0
y = -2x + 4
therefore m = -2
Let m1 is the slope of L1
m x m1 = -1
(-2)m1 = -1
m1 = 1/2
Let L1 is y=m1x + c
where m1 is the slope of L1 and C is the y-intercept
y = 0.5x + c
Substitue A to L1
0 = 0.5(2) + c
c = -1
Therefore L1 : y = 0.5x -1
2y=x - 2
x+2y + 2 = 0
c) let L2 : y = mx + c
becasue L2// x - axis , m = 0
y = c
Substitue B to y =c
y = 4
L1 : x+2y + 2 = 0
L2: y = 4
Substitue L2 to L1
x + 2(4) + 2 = 0
x + 10 = 0
x = -10
Therefore C ( -10, 4)
A coordinate is (x,0)
Substitue B to L
2(0) + y - 4 = 0
y - 4 = 0
y = 4
Substitue A to L
2x + 0 - 4 = 0
2x = 4
x = 2
therefore B (0,4) and A (2,0)
b) Firstly, find the slope of L
Let m is the slope of L
2x + y - 4 = 0
y = -2x + 4
therefore m = -2
Let m1 is the slope of L1
m x m1 = -1
(-2)m1 = -1
m1 = 1/2
Let L1 is y=m1x + c
where m1 is the slope of L1 and C is the y-intercept
y = 0.5x + c
Substitue A to L1
0 = 0.5(2) + c
c = -1
Therefore L1 : y = 0.5x -1
2y=x - 2
x+2y + 2 = 0
c) let L2 : y = mx + c
becasue L2// x - axis , m = 0
y = c
Substitue B to y =c
y = 4
L1 : x+2y + 2 = 0
L2: y = 4
Substitue L2 to L1
x + 2(4) + 2 = 0
x + 10 = 0
x = -10
Therefore C ( -10, 4)
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