SOLUTION: Use the midpoint formula method to find the equation of the perpendicular bisector of th the line segment whose endpoints are (-2, 2) and (6, 4). Write the equation in general form

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Question 1156996: Use the midpoint formula method to find the equation of the perpendicular bisector of th the line segment whose endpoints are (-2, 2) and (6, 4). Write the equation in general form
please show steps thank you!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Find the slope of the given line segment
+m%5B1%5D+=+%28+4+-+2+%29+%2F+%28+6+-%28-2%29+%29+
+m%5B1%5D+=+2+%2F+8+
+m%5B1%5D+=+1%2F4+
----------------------------
Any line perpendicular to this line has slope =
+m%5B2%5D+=+-1%2Fm%5B1%5D+
+m%5B2%5D+=+-1%2F%281%2F4%29+
+m%5B2%5D+=+-4+
---------------------------
( -2,2 )
( 6, 4 )
The x-value of the midpoint is:
+x%5Bm%5D+=+%28+6+%2B%28-2%29+%29+%2F+2+
+x%5Bm%5D+=+4%2F2+
+x%5Bm%5D+=+2+
The y-value of the midpoint is:
+y%5Bm%5D+=+%28+4+%2B+2+%29+%2F+2+
+y%5Bm%5D+=+6%2F2+
+y%5Bm%5D+=+3+
The midpoint is at ( 2, 3 )
--------------------------------
Use the general point-slope formula:
+%28+y+-+3+%29+%2F+%28+x+-+2+%29+=+-4+
+y+-+3+=+-4%2A%28+x+-+2+%29+
+y+-+3+=+-4x+%2B+8+
+y+=+-4x+%2B+11+
In general form:
+4x+%2B+y+=+11+
----------------------------
check:
does it go through ( 2,3 ) ?
+3+=+-4%2A2+%2B+11+
+3+=+-8+%2B+11+
+3+=+3+
OK
Check the math & get a 2nd opinion if needed