194. In the rectangular coordinate system above, the line
y = x is the perpendicular bisector of segment AB (not
shown), and the x-axis is the perpendicular bisector of
segment BC (not shown). If the coordinates of point A
are (2,3), what are the coordinates of point C ?
(A) (-3,-2)
(B) (-3,2)
(C) (2,-3)
(D) (3,-2)
(E) (2,3)
y = x is the perpendicular bisector of segment AB (not
shown), and the x-axis is the perpendicular bisector of
segment BC (not shown). If the coordinates of point A
are (2,3), what are the coordinates of point C ?
(A) (-3,-2)
(B) (-3,2)
(C) (2,-3)
(D) (3,-2)
(E) (2,3)
the line y=x can bisect line segment AB only if the angle in the point of bisection is 90`. So this will make another side equal to Srt(13) which can be easily found from A (2;3) - but forget this now; we need another line to be equal to A-O origin line segment - this could be B (2;3) for having angle in the point of bisection =90`. The question further suggests that BC is also bisected by abscess x. It's only possible when the same line segment portion lies below y=0 or C (3;-2) and answer D.
