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Let L1 be the perpendicular bisector and L2 be the bisected line, as shown in the figure.
Given that the equation of the bisector L1 is 8y+5x=4,
=> y=-5/8x+1/2
Let m_1 be the slope of L1, and m_2 the slope of L2,
=> m_1=-5/8
Recall that the product of the slopes of two perpendicular lines is -1,
=> m_2xxm_1=-1, => m_2=8/5
=> equation of L2 is : y-7=8/5(x-2)
=> y=8/5x+(19)/5
Set the equations of L1 and L2 equal to each other to find the intersection point P(x_m, y_m), which is also the midpoint of L2.
=> -5/8x+1/2=8/5x+19/5
=> x=-(132)/(89)
=> y=-5/8x+1/2=-5/8xx(-(132)/(89))+1/2=(127)/(89)
=> P(x_m,y_m)=(-(132)/(89), (127)/(89))
Let the other end point of L2 be B(x,y),
Since P is the midpoint of L2,
=> ((x+2)/2, (y+7)/2) = (-(132)/(89), (127)/(89))
=> (x,y)=(-(442)/(89), -(369)/(89))
