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locus of points such 3 points are collinear, in space (Chile 2016 L2 P6)

Source:

May 31, 2019

geometryLocus3D geometryLocus problemscollinear

Problem Statement

Let

P_1

and

P_2

be two non-parallel planes in space, and

A

a point that does not It is in none of them. For each point

X

, let

X_1

denote its reflection with respect to

P_1

, and

X_2

its reflection with respect to

P_2

. Determine the locus of points

X

for the which

X_1, X_2

and

A

are collinear.