SOLUTION: A line segment has one endpoint at P(3, -1) and a midpoint of M(5, 4) What is the value of the other endpoint?

Algebra ->  Formulas -> SOLUTION: A line segment has one endpoint at P(3, -1) and a midpoint of M(5, 4) What is the value of the other endpoint?       Log On


   

Question 1153137: A line segment has one endpoint at P(3, -1) and a midpoint of M(5, 4) What is the value of the other endpoint?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
P( 3, -1 )
M( 5, 4 )
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Find x-value of the other endpoint L( x, y )
+%28+3+%2B+x+%29+%2F+2+=+5+
+3+%2B+x+=+10+
+x+=+7+
-----------------
+%28+-1+%2B+y+%29+%2F+2+=+4+
+-1+%2B+y+=+8+
+y+=+9+
--------------------
L( x, y ), the other endpoint, is L( 7, 9 )
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check answer:
Find the equation that goes through P and L
+%28+y+-%28-1%29+%29+%2F+%28+x+-+3+%29+=+%28+9+-%28-1%29+%29+%2F+%28+7+-+3+%29+
+%28+y+%2B+1+%29+%2F+%28+x+-+3+%29+=+%28+9+%2B+1+%29+%2F+%28+7+-+3+%29+
+%28+y+%2B+1+%29+%2F+%28+x+-+3+%29+=+10+%2F+4+
+%28+y+%2B+1+%29+%2F+%28+x+-+3+%29+=+5%2F2+
+2%2A%28+y+%2B+1+%29+=+5%2A%28+x+-+3+%29+
+2y+%2B+2+=+5x+-+15+
+2y+=+5x+-+17+
+y+=+%285%2F2%29%2Ax+-+17%2F2+
Does the line go through M( 5,4 ) ?
+4+=+%28+5%2F2+%29%2A5+-+17%2F2+
+4+=+25%2F2+-+17%2F2+
+4+=+8%2F2+
+4+=+4+
OK