SOLUTION: Point P is on the directed line segment from point X(−6, −2) to point Y(6,7) and divides the segment in the ratio 1:5. What are the coordinates of point P?

Algebra ->  Geometry-proofs -> SOLUTION: Point P is on the directed line segment from point X(−6, −2) to point Y(6,7) and divides the segment in the ratio 1:5. What are the coordinates of point P?      Log On


   

Question 1066355: Point P is on the directed line segment from point X(−6, −2) to point Y(6,7) and divides the segment in the ratio 1:5. What are the coordinates of point P?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The point P will be 1/6 of the way from X to Y
For the X coordinate:
+1%2F6+=+%28+X%5Bp%5D+-%28-6%29+%29+%2F+%28+6+-%28-6%29+%29+
+1%2F6+=+%28+X%5Bp%5D+%2B+6+%29+%2F+12+
+2+=+X%5Bp%5D+%2B+6+
+X%5Bp%5D+=+-4+
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For the Y coordinate:
+1%2F6+=+%28+Y%5Bp%5D+-%28-2%29+%29+%2F+%28+7+-%28-2%29+%29+
+1%2F6+=+%28+Y%5Bp%5D+%2B+2+%29+%2F+9+
Multiply both sides by +18+
+3+=+2%2A%28+Y%5Bp%5D+%2B+2+%29+
+3+=+2Y%5Bp%5D+%2B+4+
+2Y%5Bp%5D+=+-1+
+Y%5Bp%5D+=+-1%2F2+
------------------
The point P is P( -4, -1/2 )
Check my math & get another
opinion if needed