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Question 837215: sir please help me i badly need it now.. thanks..
Find the equation of the line through (-3,5) which makes the angle of 45 degrees with the line 2x+y=12 . its analytic geometry sir..
Answer by LinnW(1048)   (Show Source):
You can put this solution on YOUR website!
Let's find the equation of a line through (-3,5)
that is perpendicular to y = -2x + 12
First find the slope of 2x + y = 12
add -2x to each side
y = -2x + 12
slope is -2
so slope of perpendicular is 1/2
To find the slope of a line that is 45 degrees
offset, consider equations with slopes -2 and 1/2
the pass through (0,0)
y =-2x and y = (1/2)x
Let L = the length of the segment between
(0,0) and (1,-2) , points on the line y = -2x
The length of the segment between
(0,0) and (2,1) is equal L and on the line y = (1/2)x
The segment between (0,0) and the midpoint
between (1,-2) and (2,1) will bisect the two lines
and the angle will be 45 degrees from each.
The midpoint is ( (1+2)/2 , (-2+1)/2 )
= ( 3/2 , -1/2)
The slope of the line through (0,0) and ( 3/2 , -1/2 )
is (-1/2)/(3/2) = -1/3
A line though (-3,5) with a slope of -1/3 will
be 45 degrees offset from 2x+y=12
y = mx + b
5 = (-1/3)(-3) + b
5 = 1 + b
4 = b
Our equation is y = (-1/3)x + 4
Check out the following link to see the plot.
http://www.wolframalpha.com/input/?i=plot+y%3D-x%2F3+%2B4++and+2x%2By%3D12
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