What are the coordinates of point B?

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Discussion Overview

The discussion revolves around determining the coordinates of point B given specific conditions about midpoints and quadrants. It includes both conceptual understanding of midpoints and practical application in solving coordinate geometry problems.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant expresses confusion about a problem involving midpoints and quadrants, seeking assistance.
  • Another participant suggests visualizing the problem by drawing a line from point Q in Quadrant II to the origin to determine the quadrant for point S.
  • A third participant proposes that point S lies in Quadrant IV, indicating a potential understanding of the problem.
  • A later reply explains the general formula for finding the midpoint and applies it to find the coordinates of point B, concluding that B is at (-2, -6).

Areas of Agreement / Disagreement

There is no consensus on the quadrant for point S, as one participant suggests Quadrant IV while another has not confirmed this. The calculation for point B appears to be accepted by at least one participant, but the overall discussion remains unresolved regarding the quadrant question.

Contextual Notes

The discussion does not clarify the assumptions regarding the placement of points or the implications of the midpoint formula in relation to the quadrants.

xowe
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Erm, I have another problem. This question confused me, I'm not sure how to do it. Help would be apprecaited. Thanks
The midpoint of line QS is the origin. Point Q is located in Quadrant II. What quadrant contains point S?
Same with this one.
M(5,12) is the midpoint of line AB. The coordinates of point A are (2,6). What are the coordinates of point B?
 
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Draw a picture. Take a point Q in the second quadrant, and draw a line from Q to the origin. Into which quadrant can you extend the line (so that it is still straight)? Now, which quadrant must S lie in?
 
Quadrent 4 I think. Ok, I think I get it. Thanks
 
In general, the midpoint of the line segment from (x0,y0) to (x1,y1) is the "average" of the two: ((x0+x1)/2, (y0+y1)/2).

In this case you are told that the midpoint of the line segment from A:(2,6) to the point B (call its coordinates (x,y)) is (0,0). That is (2+ x)/2= 0 and (6+y)/2= 0. It should be easy to see that B is (-2, -6).
 

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