Justin J.

asked • 06/06/15

Equations and Midpoints

We are driving diagonally cross country from Portland, OR, to city Southeast in the USA. We know that the midpoint of out drive can be represent as (x1+x2)/2, (y1+y)/2. If we know that x1=500&y1=200, what would be the midpoint if y2=600?(and we require (x1+y2)/2

Casey W.

tutor
what do you mean you require (x_1+y_2)/2??
 
If y_2=600 and y_1=200, then we have traveled 400 units North (or south) between our start and end...so the middle or average vertical position is given by (y_1+y_2)/2=400...
 
So the midpoint lies at ((x_1+x_2)/2,400).
 
If the assumption about driving diagonally is meant to imply that the distance traveled East/West (in the x direction) is equal to the distance traveled North/South (in the y direction), then the line we are traveling along has slope= +/-1...and thus the x_2 would be either 900 or 100, and the midpoint would be at (900,400) or (100,400)...depending on how you define the directions in this situation.  Clearly you have increased y going from y_1 to y_2, but we were supposed to be moving SOUTH and East from Portland to Southeast city...so perhaps there is something a little off in the problem.
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06/06/15

Justin J.

Yes, I did write the problem wrong. It should be: We are driving diagonally cross country from Portland, OR, to a city Southeast in the USA. We know that the midpoint of our drive can be represented as (x1+x2)/2, (y1+y2)/2. If we know that x1=500&y1=200, what would be the midpoint if y2=600?(and we require (x1+y1)=(x2+y2))
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06/06/15

1 Expert Answer

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Juliet T. answered • 06/07/15

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Certified Singapore PreK-12 Math Teacher, over 20 years of experience
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Hi Justin, hope that the following will help you with the question.
 
Since we require (x1+y1)=(x2+y2) and we have x1 = 500, y1 = 200 and y2 = 600,
putting the values into 
x1+y1 = x2+y2 gives us
500 + 200 = x2 + 600.
So, x2 = 500 + 200 - 600
           = 100
 
Since midpoint is ( (x1+x2)/2, (y1+y2)/2 ) and we have x1 = 500, y1 = 200, x2 = 100 and y2 = 600,
putting the values into 
( (x1+x2)/2, (y1+y2)/2 ) gives us
( (500 +100)/2, (200 + 600)/2) = (300, 400)
 
In conclusion, the midpoint is (300, 400).
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