SOLUTION: The equation of the gas line is 2x+y=2 . a factory located at the point ( 6,7) will connect with the gas line perpendicularly . find the equation of the connecting line and the len
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Question 736421: The equation of the gas line is 2x+y=2 . a factory located at the point ( 6,7) will connect with the gas line perpendicularly . find the equation of the connecting line and the length of the pipe required if the units are miles . Answer by mananth(16946) (Show Source):
1 y = -2 x + 2
Divide by 1
y = -2 x + 2
Compare this equation with y=mx+b, m= slope & b= y intercept
slope m = -2
The slope of a line perpendicular to the above line will be the negative reciprocal 1/2
Because m1*m2 =-1
The slope of the required line will be 1/2
m= 1/2 ,point ( 4 , 7 )
Find b by plugging the values of m & the point in
y=mx+b
7 = 2 + b
b= 5
m= 1/2
The required equation is y = 1/ 2 x + 5
where do they intersect
2.00 x + 1.00 y = 2.00 .............1
Total value
-0.50 x + 1.00 y = 5.00 .............2
Eliminate y
multiply (1)by -1.00
Multiply (2) by 1.00
-2.00 x -1.00 y = -2.00
-0.50 x + 1.00 y = 5.00
Add the two equations
-2.50 x = 3.00
/ -2.50
x = -1.20
plug value of x in (1)
2.00 x + 1.00 y = 2.00
-2.40 + y = 2.00
y = 2.00 + 2.40
y = 4.40
y = 4.40
(-1.20,4.40) (6,7)
Find the distance between the points. that's the length of the pipe line
Distance between two points
x1 y1 x2 y2
