In the xy-plane, the origin O is the midpoint of line segment PQ. If the coordinates of P are (r,s), what are the coordinates of Q ?
A. (r,s)
B. (s,-r)
C. (-s,-r)
D. (-r,s)
E. (-r,-s)
E
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OG In the xy-plane, the Origin is the midpoint
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AbeNeedsAnswers
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If we've got two points (a, b) and (c, d), then their midpoint = ((a + b)/2, (c+d)/2).
Since the origin has the coordinates (0, 0), we need (a + b) = 0 and (c + d) = 0. This is possible with (r + -r) and (s + -s), so our missing coordinate is (-r, -s).
Since the origin has the coordinates (0, 0), we need (a + b) = 0 and (c + d) = 0. This is possible with (r + -r) and (s + -s), so our missing coordinate is (-r, -s).
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Hi AbeNeedsAnswers,
We're told that the origin O is the MIDPOINT of line segment PQ and that the coordinates of P are (r,s). We're asked for the coordinates of Q. This question can be solved by TESTing VALUES.
IF... Point P = (r,s) = (2,1)...
then Point Q would be (-2, -1). That equates to (-r,-s).
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
We're told that the origin O is the MIDPOINT of line segment PQ and that the coordinates of P are (r,s). We're asked for the coordinates of Q. This question can be solved by TESTing VALUES.
IF... Point P = (r,s) = (2,1)...
then Point Q would be (-2, -1). That equates to (-r,-s).
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
If we have two points A=(x1,y1) and B=(x2,y2), then the midpoint of the line segment AB is
M= ( (x1+x2) / 2 , (y1+y2 )/ 2 ).
As the Origin is the Midpoint fo the line segment PQ, we have that M= (0,0).
Let's say that A=P, i.e. x1=r and x2=s. We want to calculate the coordinates of Q=(x2,y2).
So, we have: (0,0) = ( (r+x2)/2 , (s+y2)/2 ) which implies (r+x2)/2 = 0 and (s+y2)/2 = 0.
This is equivalent to r+x2=0 and s+y2=0.
Finally, we get x2=-r and y2=-s, i.e Q=(-r,-s).
So, the correct option is E
M= ( (x1+x2) / 2 , (y1+y2 )/ 2 ).
As the Origin is the Midpoint fo the line segment PQ, we have that M= (0,0).
Let's say that A=P, i.e. x1=r and x2=s. We want to calculate the coordinates of Q=(x2,y2).
So, we have: (0,0) = ( (r+x2)/2 , (s+y2)/2 ) which implies (r+x2)/2 = 0 and (s+y2)/2 = 0.
This is equivalent to r+x2=0 and s+y2=0.
Finally, we get x2=-r and y2=-s, i.e Q=(-r,-s).
So, the correct option is E
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We can let the coordinates of Q be (x, y). Since the origin (0, 0) is the midpoint of PQ, we have:AbeNeedsAnswers wrote:In the xy-plane, the origin O is the midpoint of line segment PQ. If the coordinates of P are (r,s), what are the coordinates of Q ?
A. (r,s)
B. (s,-r)
C. (-s,-r)
D. (-r,s)
E. (-r,-s)
(r + x)/2 = 0 and (s + y)/2 = 0
Multiplying each equation by 2, we have:
r + x = 0 and s + y = 0
x = -r and y = -s
Thus, the coordinates of Q are (-r, -s).
Answer: E
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