To show the elation, drag the point [i]O[/i] so that it lies on [i]o[/i]. This figure shows an elation or homology with center [i]O[/i] and axis [math]o = CP[/math] that transforms [i]A[/i] into another point [i]A'[/i] on the line [math]c=OA[/math]. Here [i]C[/i] and [i]P[/i] are arbitrary points on the axis [i]o[/i]. Let [i]p[/i] be an arbitrary line through [i]O[/i], meeting [math]b=CA[/math] and [math]b'=CA'[/math] in [i]Q[/i] and [i]Q'[/i]. Let [i]B[/i] be an arbitrary point on [i]c[/i].