DS - Coordinates

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Analyse the question stem. What is the question really asking us ?
Draw it out on your scrap paper ... draw a line CD.
The question asks about the midpoint of line CD. See snapshot attached.
So in order to find the midpoint, we need the coordinates of BOTH C and D.

Lets look at statement 1:
This doesnt tell us anything about D. So INSUFF. Remember we need BOTH coordinates C and D.

Statement 2:
This doesnt tell us anything about C. So INSUFF.

Both 1 and 2 together:
Right ... now we have both C and D, and can work out the midpoint of line CD. SUFFICIENT. answer is C. Dont forget we dont have to find the final answer ... just need to know if we have enough info to solve.

Just for completeness ... in order to find midpoint ... find the midpoint between the y-coordinates of line CD, and we find the midpoint of the x-coordinates of line CD.
So if the coordinates of C were (5,6)
and the coordinates of D were (1,3)
Then the midpoint of the y-coordinate would be (6+3)/2 = 4.5
The midpoint of the x-coordinate would be (5+1)/2 = 3
So the midpoint of CD would be (3,4.5).

Hope this makes it clear.

II.

Thank you! I guess I got confused in terms of a an db being variables -- but they are known in the stem. THanks again.

Just wondering if anyone has another approach for this type of question ... or if anyone solved it another way.

Thanks.
II

The ans is not so straight forward as you made it to be II

The formula for midpoint is (X1+X2)/2 , (Y1+Y2)/2

C = (a,1-b) we are given a>0 and b>0

D = (1-a,b) we are given a>0 and b>0

Ans is C because we can find midpoint co-ordinated that will not var a,b in them

a+1-a/2 = 1/2
1-b+b/2 = 1/2

The calculations above stand good only because we know that a>0 and b>0.

If either a or b was <0 then the ans would have been E