SOLUTION: How to find the equation of the perpendicular erected in the middle of the segment connecting the points (4,-7) and (7,-4)? Thank you very much

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Question 547180: How to find the equation of the perpendicular erected in the middle of the segment connecting the points (4,-7) and (7,-4)?
Thank you very much
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You need 2 things:
1) slope of the line segment
2) (x,y) of the midpoint
-----------------
First you find the x-coordinate of the midpoint
(4,-7) and (7,-4)
+%28+7+%2B+4+%29+%2F+2+=+11%2F2+
Now the y-coordinate
+%28+-4+%2B+%28-7%29+%29+%2F+2++=+-11%2F2+
The midpoint is at (11/2, -11/2)
--------------------------
Now find slope
slope = change in y / change in x
+m+=+%28+-4+-%28-7%29+%29+%2F+%28+7+-%28-7%29+%29+

+-%281%2Fm%29+=+-14%2F3+
-----------------
Now I can use the point-slope formula
+-14%2F3+=+%28+y+-+%28-11%2F2%29+%29+%2F+%28+x+-+11%2F2+%29+
+-14%2F3+=+%28+y+%2B+11%2F2%29+%2F+%28+x+-+11%2F2+%29+
+y+%2B+11%2F2+=+%28-14%2F3%29%2A%28+x+-+11%2F2+%29+
+y+%2B+11%2F2+=+%28-14%2F3%29%2Ax+%2B+154%2F6+
Multiply both sides by 6
+6y+%2B+33+=+-28x+%2B+154+
+6y+=+-28x+%2B+121+
+y+=+-%2814%2F3%29%2Ax+%2B+121%2F6+ answer
check:
Does it go through (11/2, -11/2) ?
+y+=+-%2814%2F3%29%2Ax+%2B+121%2F6+
+-11%2F2+=+-%2814%2F3%29%2A%2811%2F2%29+%2B+121%2F6+
+-33+=+%28-14%29%2A11+%2B+121+
+-33+=+-154+%2B+121+
+-33+=+-33+
OK
Here's a plot of the lines ( I don't know how to show a line segment,
so I show it a a continuous line