Question 1199457
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The equation of the perpendicular bisector of PQ is 4x+3y-15=0, or y=(-4/3)x+5.<br>
The slope of the perpendicular bisector is -4/3, so the slope of PQ is 3/4.<br>
I'll outline the process for solving the problem and let you fill in the details.<br>
(1) Use the given point (7,4) and the slope of 3/4 to find the equation of line PQ.
(2) Solve the pair of equations representing PQ and the perpendicular bisector to find the point of intersection.  (You should find it is (3,1); that point is the midpoint of PQ).
(3) Use the coordinates of P and the midpoint of PQ to find the coordinates of Q.  (You should find it is Q(-1,-2)).<br>