How to find the perpendicular distance from point C(0,-4) to the line with an equation 2y - 5x = 4?

C(0,-4)


line: 2y - 5x = 4





Please show the steps clearly...I am still confused on how to find perpendicular distances...








thanks for your help!!

How to find the perpendicular distance from point C(0,-4) to the line with an equation 2y - 5x = 4?
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Perpendicular is the negative recipricol slope.





+5/2 becomes -2/5





y+4 = -2/5(x)





which crosses at the common point of intersection.





5Y + 20 = -2x





5y + 2x = 20 and 2y - 5x =4 .... solve simultaneously.





times first by 5 and second by 2 then add together





29Y = 108 ..... y = 108/29





First by two and second by -5 ....





29X = 20 .... x = 29/20.





So the other point is (108/29,29/20) and then find the distance to (0,-4). Use pyth formula.
Reply:2y - 5x = 4


y=5/2 x+2


in this equation 5/2 is slope of straigt line


slope of normala on y=5/2 x+2 is


-2/5


then


y=-2/5x+k is equation of perpendicular on y=5/2 x+2


if pass by C(0,-4) then


-4=k


then obtain





y=-2/5 x-4


y=5/2x +4


then x(5/2+2/5)=-8


x=-8*10/29


find y


And now you have intersect from 2y-5x=4 and


y=-2/5 x-4


distance from C(0,-4) and this point is


sqrt((0-x)^2+(-4-y)^2)


where x,y are coordonate of intersection
Reply:Given: C(0,-4) and line: 2y - 5x = 4 or 5x - 2y + 4





From analytical geometry:





d = |Ax1 + By1 + C|/√(A^2 + B^2)





where x1 = 0, y1 = -4


A = 2, B = -5, and C = 4





Substitute the values in the above formula for distance between a point and a line:





d = |(2)(0) + (-5)((-4) + 4|/√[(2^2 + (-5)^2]


d = 4.46 ANSWER





Hope I help you.





teddy boy
Reply:us the qudratic formula -b+/-(rootb^2-4ac)/2a then multiply by the diffirentiate the commen difference, Leaving you with the fact that you have no friends and will probably die a virgin.


(sorry that was a bad joke) If you need any tips i would go to www.mudfall.com - it realy helped me understand perpendicular distances - and its pretty easy to follow.
Reply:first write the equation like this--


5x-2y+4=0





now , put x=0 and y= -4 and divide it by sqrt of ( sqaure of 5 + square of 2)