y=-2x+6 is the perpendicular bisector of the line segment AB. If A has coordinates (7,2) what are the coordinates for B?
This is how i set it up
perp bisector ==> neg reciprical
-2 ==> +1/2
y=1/2 x + b
2=1/2 (7) +b
2 = 3.5 + b
therefore line AB is defined as ===> y = 1/2X - 1.5
set the 2 equations together to get their midpoint
-2x+6 = 1/2x - 1.5
-2.5x = -7.5
how do we get Y?
If -2 is the slope of the bisector than 1/2 is the slope of the line segment.
now we need to find the y intercept if we haveone. y=x/2+B use A's coordinates.
2=7/2+B B=-3/2 so now we have y=x/2-3/2
to find B:
u gotta find where the two lines intersect: x/2-3/2=-2x+6
-15/2=-5x/2 ---> 15/2=5x/2 ---> x=3, thus y=0.
Essentially 3,0 is the midpoint of line segment A,B. So since 7 is 4 away from 3, just subtract 3 by 4. We get -1 for x. and y use same logic. we get -2.