If a and b are positive numbers , what are the coordinates of the midpoint of the line segment CD in the xy-plane ?

1) The coordinates of C are ( a , 1-b)

2) The coordinates 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