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Question: we say that points x and y are symmetric points...

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We say that points X and Y are symmetric points with respect to point M if Mis the midpoint of segment XY. Given AABC, suppose that is a line not parallel to any of its sides, and let P Q, and R be the points of intersection of l with lines BC, and respectively. Suppose that points P and X are symmetric with respect to the midpoint of segment BC. Similarly, assume that Q and Yare symmetric with respect to the midpoint of CA ad that R and Z are symmetric with respect to the midpoint of AB. Show that X, Y and Z are collinear. In the case that I passes through a vertex of the triangle, which line passes through Y, and Z?

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