SOLUTION: A line segment has endpoints L(-2,3) and N(6,11). The point M is the midpoint of LN. What is an equation of a line perpendicular to LN and passing through M?

Algebra ->  Coordinate-system -> SOLUTION: A line segment has endpoints L(-2,3) and N(6,11). The point M is the midpoint of LN. What is an equation of a line perpendicular to LN and passing through M?      Log On


   

Question 973859: A line segment has endpoints L(-2,3) and N(6,11). The point M is the midpoint of LN. What is an equation of a line perpendicular to LN and passing through M?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+x%5BM%5D=+%28+6+%2B%28-2%29+%29+%2F+2+
+x%5BM%5D+=+4%2F2+
+x%5BM%5D+=+2+
----------------
+y%5BM%5D+=+%28+11+%2B+3+%29+%2F+2+
+y%5BM%5D+=+14%2F2+
+y%5BM%5D+=+7+
----------------
The midpoint of the line LN is at ( 2,7 )
Now find slope of line LN
+m+=+%28+11+-+3+%29+%2F+%28+6+-%28-2%29+%29+
+m+=+8+%2F+8+
+m+=+1+
----------------
Any line perpendicular to LN will have
slope = +-1%2Fm+=+-+1%2F1+
slope = +-1+
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Now use general point-slope formula:
+%28+y+-+7+%29+%2F+%28+x+-+2+%29+=+-1+
+y+-+7+=+-1%2A%28+x+-+2+%29+
+y+-+7+=+-x+%2B+2+
+y+=+-x+%2B+9+ answer
----------------------
check:
does it go through ( 2,7 )?
+7+=+-2+%2B+9+
+7+=+7+
OK