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smc

geometry senior

Problem

Segments , , are drawn from the vertices of triangle , each perpendicular to a straight line , not intersecting the triangle. Points , , are the intersection points of with the perpendiculars. If is the length of the perpendicular segment drawn to from the intersection point of the medians of the triangle, then is:
(A)
(B)
(C)
(D)
Solution
WLOG let be the x-axis, or at least horizontal. The three lengths represent the y-coordinates of points . As is by definition the average of , it's coordinates are the average of the coordinates of and . Hence, the y-coordinate of , which is also the distance from to , is the average of the y-coordinates of and , or , hence the result.
Final answer
A