Question 168522
# 1


X-coordinate of the midpoint: average of the two x coordinates


x-mid = (5+(-2))/2 = 3/2 = 1.5



Y-coordinate of the midpoint: average of the two y coordinates


y-mid = (1+7)/2 = 8/2 = 4



Midpoint between the points A(5,1) and B(-2,7): (1.5, 4)



Note: you can graph the points and measure the distances to verify




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# 2



Use the same technique used in problem #1 to get the midpoint (4, 4)



Now find the slope between the the points (2,2) and (6,6)



Whatever that slope turns out to be, find the reciprocal (ie flip the fraction) and change the sign to find the perpendicular slope. For instance if the slope is 1/2, then flip and change the sign to get -2/1. 


Once you have the perpendicular slope, plug it into the equation



{{{y-y[1]=m( x-x[1] )}}} where in this case {{{m}}} is the perpendicular slope and *[Tex \LARGE \left(x_{1},y_{1}\right)] is the midpoint


From there, solve for "y" to find the equation of the perpendicular bisector




Feel free to ask for further help in finding the perpendicular bisector.