In xy plane, line K passes through the points A(6, -7) and B(4, 5). Does line K also pass through point C?
Coordinates of Point C are ( 5, -1)
Point C is equidistant from Point A and Point B.
I don't quite understand this.. can someone please explain clearly?
Using the given information, we know an equation for the line K is y+7=((-7-5)/(6-4))(x-6)=-6*(x-6). Given an equation for the line, the coordinates of any point on the xy-plane are sufficient to determine whether it is on the line. Hence, statement 1 is sufficient. Statement 2 is not sufficient because any point on the line perpendicular to K passing through the midpoint of AB is equidistant from A and B. Clearly the midpoint of AB lies on AB but the other points do not. The answer is A.