find the line of reflection for the points A(3,12) and A'(7,18)

Question

I don't know how to find the line of reflection when only given points. . . please help?

Answer 1

The line of reflection has to be perpendicular bisector of the line AA'.

The slope of AA' is (18-12)/(7-3)=6/4=3/2

The slope of line M= -2/3

The midpoint of |AA'| is (5,15)

The equation of line M: 15=-2/3 x 5 +b

15= -10/3 +b

18 1/3=b

y=(-2/3)x+18  1/3 (in slope, y-intercept form)

or 2x+3y=55