SOLUTION: The perpendicular bisector of the line segment AB is the line that passes through the midpoint of AB and is perpendicular to AB. The equation of the perpendicular bisector of the

Algebra ->  Graphs -> SOLUTION: The perpendicular bisector of the line segment AB is the line that passes through the midpoint of AB and is perpendicular to AB. The equation of the perpendicular bisector of the       Log On


   



Question 1061714: The perpendicular bisector of the line segment AB is the line that passes through the midpoint of AB and is perpendicular to AB. The equation of the perpendicular bisector of the line segment joining the points (1,2) and (-5,12) is y=mx+b. Find m+b.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+x%5Bmid%5D+=+%28+1+-+5+%29%2F2+
+x%5Bmid%5D+=+-2+
and
+y%5Bmid%5D+=+%28+2+%2B+12+%29%2F2+
+y%5Bmid%5D+=+7+
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The slope of the line segment is:
+%28+12+-+2+%29+%2F+%28+-5+-+1+%29+=+10%2F%28-6%29+
+10%2F%28-6%29+=+-5%2F3+
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The required line goes through ( -2, 7 )
and has slope = +-5%2F3+
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Use the point-slope formula
+%28+y+-+7+%29+%2F+%28+x+-%28-2%29++%29+=+-5%2F3+
+y+-+7+=+%28-5%2F3%29%2A%28+x+%2B+2+%29+
+y+-+7+=+%281%2F3%29%2A%28+-5x+-+10+%29+
+y+=+%28-5%2F3%29%2Ax+-+10%2F3+%2B+7+
+y+=+%28-5%2F3%29%2Ax+-10%2F3+%2B+21%2F3+
+y+=+%28-5%2F3%29%2Ax+%2B+11%2F3+
+m+%2B+b+=+-5%2F3+%2B+11%2F3+
+m+%2B+b+=+2+
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check answer:
does the line go through ( -2,7 ) ?
+y+=+%28-5%2F3%29%2Ax+%2B+11%2F3+
+7+=+%28-5%2F3%29%2A%28-2%29+%2B+11%2F3+
+21+=+10+%2B+11+
+21+=+21+
OK