vinni.k wrote:In xy plane, line K passes through the points A(6, -7) and B(4, 5). Does line K also pass through point C?
(1). Coordinates of Point C are ( 5, -1)
(2). Point C is equidistant from Point A and Point B.
Target question:
Does line K pass through point C?
Given: line K passes through the points A(6, -7) and B(4, 5)
NOTE: Once we know two points on line K, we
could find the equation of the line, and we
could also accurately draw the line on the x-y coordinate plane.
Statement 1: Coordinates of Point C are ( 5, -1)
From the given information, we
could accurately draw the line on the x-y coordinate plane.
This would allow us to
definitely determine whether or not K passes through point C.
In other words, the information in statement 1 allows us to answer the
target question with certainty, which means statement 1 is SUFFICIENT
Statement 2: Point C is equidistant from Point A and Point B.
In other words, point C is such that, we can draw a circle with point C as the center and points A and B as points on the circle (since all points on a line are equidistant from the center).
If we know that line K passes through points A and B (on the circle), can we determine whether or not line K passes through point C (the center)? No.
It could be the case that points A and B are such that
line K passes through point C.
Or it could be the case that points A and B are such that
line K does not pass through point C.
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer =
A
Cheers,
Brent
