Find if the distance between the point (2, y) and the line 3x-4y+5 = 0 is 12 units. Find y
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calendarEducator since 2010
write12,554 answers
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The distance between a point (x1, y1) and a line ax + by + c = 0 is given by: |a*x1 + b*y1 + c|/sqrt (a^2 + b^2)
Substituting the values we have here
D = |a*x1 + b*y1 + c|/sqrt (a^2 + b^2)
=> |3*2 - 4*y + 5|/sqrt (3^2 + 4^2)
=> |6 - 4y + 5|/ sqrt 25
Now D = 12
=> 60 = |11 - 4y|
=> 11 -4y = 60 and 11 - 4y = -60
=> 4y = -49 and -4y = -71
=> y = -49/4 and y = 71/ 4
The values of y are y = -49/4 and y = 71/ 4
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calendarEducator since 2008
write3,662 answers
starTop subjects are Math, Science, and Social Sciences
We will use the distance between a line and a point formula to find y.
We know that :
D = l ax + by + c l / sqrt(a^2 + b^2)
Now we have D = 12, a = 3 b= -4 c = 5 x = 2 and y= y
Now we will substitute.
==> 12 = l 3*2 -4*y + 5 l / sqrt( 9+16)
=> 12 = l 11 -4yl / 5
Multiply by 5.
==> l 11-4y l = 60
Now we have 2 cases.
==> case(1) : (11-4y) = 60
==> -4y = 49 ==> y= -49/4
==> case(2) : -(11-4y) = 60
==> -11 + 4y = 60
==> 4y = 71
==> y= 71/4
Then the values of y = { 71/4, -49/4}