MGMAT SG4, Guide Book 5 Chapter 8 # 7

[cyoo1987]

#7 A line represented by the equation y= -2x+6 is the perpendicular bisector of the line segment AB. IF A has the coordinates (7,2) what are the coordinates for b?

I understand in order to do this problem, you must first find the slope of AB which is equal to 1/2. Making the linear equation for AB equal to y=1/2x+b. After plugging in the coordinates for a, i ended up with y=0.5x-1.5

Then I set the two equations equal to each other and solved for x which was equal to 3.

here is where i got confused. the answer states that the midpoint for A and B are 3, 0. but im not sure where the 0 came from. can someone help? :)

[tim]

plug 3 in for x in either equation, and y will be 0, so the point we are concerned with is (3,0)

[cschmidlapp]

Separate question on this: why can you plug in the coordinates of point A (7,2) to find the y-intercept for the perpendicular bisector (which should not go through point A because it is bisecting line AB)?

Thanks

[RonPurewal]

Separate question on this: why can you plug in the coordinates of point A (7,2) to find the y-intercept for the perpendicular bisector (which should not go through point A because it is bisecting line AB)?

Thanks

Check that out again; the poster is plugging in to find the equation of AB, not the equation of the bisector.

The y-intercept of the bisector is already known (it's 6; just look at the given equation), so there would be no sense in trying to "solve for" it.