Question

Find an equation describing all points P(x,y) equidistant from Q(-3,4) and R(1,-3)

 

Answer: ____ x - ____ y + ____ = ____

Answer 1

Any point P on the blue perpendicular bisector of QR (red) forms an isosceles triangle PQR so that PQ=PR.

First find the midpoint ((-3+1)/2,(4-3)/2)=(-1,½). This point is on the required line. QR has a slope (4-(-3))/(-3-1)=-7/4 so the perpendicular bisector of QR has a slope of 4/7 and must pass through (-1,½). We can write the equation of the bisector y-½=(4/7)(x+1), y-½=4x/7+4/7. Multiply through by 14:

14y-7=8x+8, which in general form is 8x-14y+15=0.