SOLUTION: A line through (1,-2) and (3,1) is perpendicular to a line through (2,y) and (1,-2). Find the value of y.

Algebra ->  Proportions -> SOLUTION: A line through (1,-2) and (3,1) is perpendicular to a line through (2,y) and (1,-2). Find the value of y.      Log On


   

Question 965226: A line through (1,-2) and (3,1) is perpendicular to a line through (2,y) and (1,-2). Find the value of y.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Slope of line through ( 1,-2 ) and ( 3, 1 ):
+%28+1+-%28-2%29+%29+%2F+%28+3+-+1+%29+=+3%2F2+
------------------------------------
Slope of line through ( 2,y ) and ( 1, -2 ) :
+%28+y+-%28-2%29+%29+%2F+%28+2+-+1+%29+=+%28+y+%2B+2+%29%2F1+
+%28+y+%2B+2+%29%2F1+=+y+%2B+2+
--------------------------
If the 1st slope is +m%5B1%5D+ and the 2nd
slope is +m%5B2%5D+, then to be perpendicular
to each other:
+m%5B2%5D+=+-1%2Fm%5B1%5D+ , so I can say:
+y+%2B+2+=+-%28+1%2F%283%2F2%29+%29+
+y+%2B+2+=+-2%2F3+
+y+=+-2%2F3+-+6%2F3+
+y+=+-8%2F3+
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check answer:
+m%5B2%5D+=++%28+y+-%28-2%29+%29+%2F+%28+2+-+1+%29+
+m%5B2%5D+=+%28+-8%2F3+-%28-2%29+%29+%2F+1+
+m%5B2%5D+=+%28+-8%2F3+%2B6%2F3+%29+%2F+1+
+m%5B2%5D+=+-2%2F3+
OK