paresh_patil wrote:a & b are positive numbers. What are the co-ordinates of midpoint of segment CD in xy plane?

1) co-ordinates of C are (a,1-b)

2) co-ordinates of D are (1-a,b)

To determine the coordinates of the midpoint of a line segment, we need to know the coordinates of both the endpoints of the segment. Hence, none od the statements are individually sufficient. Let's check whether together they are sufficient or not.

1 & 2 Together: x-coordinate of the midpoint = (x-coordinate of C + x-coordinate of D)/2 = (a + 1 - a)/2 = 1/2
y-coordinate of the midpoint = (y-coordinate of C + y-coordinate of D)/2 = (1 - b + b)/2 = 1/2

Sufficient
The correct answer is C.

paresh_patil wrote:a & b are positive numbers. What are the co-ordinates of midpoint of segment CD in xy plane?

1) co-ordinates of C are (a,1-b)

2) co-ordinates of D are (1-a,b)

Target question: What are the co-ordinates of midpoint of segment CD

If we have two points (x1 , y1) and (x2, y2), then the midpoint of this points will be [(x1 + x2)/2 , (y1 + y2)/2]

In other words, to find the midpoint, we find the average of the x-coordinates and the average of the y-coordinates.

Statement 1: co-ordinates of C are (a,1-b)
Since we have no information about point D, there's no way we can find the midpoint of CD.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: co-ordinates of D are (1-a,b)
Since we have no information about point C, there's no way we can find the midpoint of CD.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
We have C(a,1-b) and D(1-a,b), so the midpoint is [(a + 1-a)/2 , (1-b + b)/2]
When we simplify, we get (1/2 , 1/2)
Since we can now answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent