Given triangle ABC with coordinates A(−4, 4), B(−4, 1), and C(−6, 0), and its image A′B′C′ with A′(0, 0), B′(−3, 0), and C′(−4, −2), find the line of reflection.
The line of reflection is the perpendicular bisector of segment AA', so passes through point (A+A')/2 = (-2, 2) and is perpendicular to the line through A and A'. That line is y = -x, so the point-slope equation of the line of reflection is ...
