If a and b are positive numbers, what are the coordinates of the midpoint of line segment CD in the xy-plane?
a) The coordinates of C are (a, 1-b)
b) The coordinates of D are (1-a, b)
Points on a graph
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Target question: What are the co-ordinates of midpoint of segment CDIf 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)
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
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The midpoint between two points is the average of the x-coordinates and the average of the y-coordinates:Rastis wrote:If a and b are positive numbers, what are the coordinates of the midpoint of line segment CD in the xy-plane?
a) The coordinates of C are (a, 1-b)
b) The coordinates of D are (1-a, b)
midpoint = [ (x� + x₂)/2, (y� + y₂)/2 ].
Clearly, neither statement alone is sufficient.
Statements combined:
midpoint = [ (a + 1-a)/2 , (1-b + b)/2 ] = (1/2, 1/2).
SUFFICIENT.
The correct answer is C.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
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