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June 8th, 2014, 11:25 AM  #1 
Newbie Joined: Jun 2014 From: UK Posts: 14 Thanks: 0  deriving a line's equation
I am attempting to find the equation of a 'perpendicular bisector'. So let's assume I have calculated the gradient and a point on the line correctly, they are: (1,1) with a gradient of 5 I now ought to be able to find the equation of the line [ax + by +c = 0]: y  y1 = m(x  x1) y  1 = 5 (x + 1) 5y + 5 = 5x 5 5y =  5x 5x + 5y = 0  However, apparently the right answer is x + 5y 4 so either my working are wrong or calculations to work out the properties of the 'perpendicular bisector' are wrong. [(1,1) with a gradient of 5] any thoughts? Mark 
June 8th, 2014, 11:46 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,981 Thanks: 1166 Math Focus: Elementary mathematics and beyond 
Can you post the entire problem, as given?

June 8th, 2014, 01:08 PM  #3 
Newbie Joined: Jun 2014 From: UK Posts: 14 Thanks: 0 
"A perpendicular bisector is a line which cuts another line in half, at right angles to the first line. Find the perpendicular bisector of the line PQ, where P = (2,4) and Q = (0,6). Arrange the equation of your line in the form ax + by + c = 0." So we have the mid point of PQ and can work out the gradient of the bisector line, and from there produce the line's equation. Sounds so easy... cheers, Mark 
June 8th, 2014, 03:41 PM  #4 
Member Joined: Feb 2012 From: Hastings, England Posts: 83 Thanks: 14 Math Focus: Problem Solving 
if the line goes from the point P(2,4) to Q(0,6) then the gradient is calculated as the change in y over the change in x, which is 10/2=5 you have found the midpoint correctly which is (1,1) the gradient of a perpendicular to a line of y=mx+c is 1/m which in this case is 1/5 = 0.2 we can now write out the equation for the perp and then fill in what we know: y=mx+c (now sub in our 0.2 for gradient of perpendicular) y=0.2x+c (now sub in the values of the midpoint for x and y) 1=0.2(1) + c (now solve to find c) 1=0.2+c c=0.8 hence equation of perpendicular is y=0.2x + 0.8 however your question wants only whole numbers, hence if we multiply by 5 we have 5y = x + 4 then add x to both sides 5y + x = 4 then subtract 4 from both sides gives 5y + x  4 = 0 hope that kind of explains it, need anything explained better or anything that's not clear let me know 
June 9th, 2014, 12:33 PM  #5 
Newbie Joined: Jun 2014 From: UK Posts: 14 Thanks: 0 
Superb! Thanks Mark 

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