SOLUTION: The point (7,4) is halfway between points A and B. If point A is on the line y=x and point B is on the line y=6, what are the coordinates of points A and B?

Algebra ->  Graphs -> SOLUTION: The point (7,4) is halfway between points A and B. If point A is on the line y=x and point B is on the line y=6, what are the coordinates of points A and B?      Log On


   

Question 1101950: The point (7,4) is halfway between points A and B. If point A is on the line y=x and point B is on the line y=6, what are the coordinates of points A and B?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let point A = ( x1 , y1 )
Let point B = ( x2 , 6 )
The midpoint is ( 7,4 )
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The x-value of the midpoint is:
(1) +%28+x%5B1%5D+%2B+x%5B2%5D+%29+%2F+2+=+7+
The y-value of the midpoint is:
(2) +%28+y%5B1%5D+%2B+6+%29+%2F+2+=+4+
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(2) +y%5B1%5D+%2B+6+=+8+
(2) +y%5B1%5D+=+2+
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For point A, +x%5B1%5D+=+y%5B1%5D+, so
(1) +%28+2+%2B+x%5B2%5D+%29+%2F+2+=+7+
(1) +2+%2B+x%5B2%5D+=+14+
(1) +x%5B2%5D+=+12+
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A( 2, 2 ) and B( 12, 6 ) are the points
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check:
(1) +%28+2+%2B+12+%29+%2F+2+=+7+
(1) +14%2F2+=+7+
(1) +7+=+7+
and
(2) +2+%2B+6+%29%2F2+=+4+
(2) +8%2F2+=+4+
(2) +4+=+4+
OK