September 3rd, 2018, 11:03 PM  #1 
Member Joined: Aug 2018 From: Nigeria Posts: 43 Thanks: 2  Analytical Geometry
The perpendicular bisector of the line AB is 3y  2x  4 = 0. If A is the point (6,5), find B's coordinates. Last edited by skipjack; September 4th, 2018 at 03:55 AM. 
September 4th, 2018, 12:01 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,204 Thanks: 511 Math Focus: Calculus/ODEs 
What is the slope of the line: $\displaystyle 3y2x4=0$ 
September 4th, 2018, 12:54 AM  #3 
Member Joined: Aug 2018 From: Nigeria Posts: 43 Thanks: 2 
m=2/3

September 4th, 2018, 04:15 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 19,700 Thanks: 1804 
Correct. That implies that AB has slope 3/2. Hence AB has equation 2y + 3x = 2*5 + 3*6 = 28. The coordinates (x, y) = (76/13, 68/13) satisfy both equations, so they are the coordinates of the midpoint of AB. Can you now find the coordinates of B? 
September 4th, 2018, 06:07 AM  #5 
Member Joined: Aug 2018 From: Nigeria Posts: 43 Thanks: 2 
Yes. Since 2MA=B 

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