Any point ppp maps to a point p'p ′ p, prime such that \overline{pp'} pp ′ start overline, p, p, prime, end overline is perpendicular to the line y=-2x+1y=−2x+1y, equals, minus, 2, x, plus, 1 and is also the diameter of a circle whose center is the intersection of \overline{pp'} pp ′ start overline, p, p, prime, end overline and y=-2x+1y=−2x+1y, equals, minus, 2, x, plus, 1.