SOLUTION: Find the point P along the directed line segment from point A(–9, 5) to point B(11, –2) that divides the segment in the ratio 4 to 1.

Algebra ->  Geometry-proofs -> SOLUTION: Find the point P along the directed line segment from point A(–9, 5) to point B(11, –2) that divides the segment in the ratio 4 to 1.      Log On


   

Question 1027408: Find the point P along the directed line segment from point A(–9, 5) to point B(11, –2) that divides the segment in the ratio 4 to 1.
Found 2 solutions by Fombitz, josmiceli:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the x distance from A to B and divide by 5.
D%5Bx%5D=%2811-%28-9%29%29=20
P is 4/5 of the distance from A to B.
P%5Bx%5D=A%5Bx%5D%2B%284%2F5%29%2820%29
P%5Bx%5D=-9%2B16
P%5Bx%5D=7
Similarly for y,
Find the y distance from A to B and divide by 5.
D%5By%5D=%28-2-%285%29%29=-7
P is 4/5 of the distance from A to B.
P%5By%5D=A%5By%5D%2B%284%2F5%29%28-7%29
P%5By%5D=25%2F5-28%2F5
P%5By%5D=-3%2F5
P:(7,-3%2F5)

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The line segments from x[A] to x[B]
and y[A] to y[B] are also divided in the ratio
4:1
---------------------
+x%5BB%5D+-+x%5BA%5D+=+11+-+%28-9%29+
+x%5BB%5D+-+x%5BA%5D+=+20+
+4%2F1+=+x+%2F+%28+20-x+%29+
+4%2A%28+20+-+x+%29+=+x+
+80+-+4x+=+x+
+5x+=+80+
+x+=+16+
---------------
+x%5BP%5D+=+x%5BA%5D+%2B+16+
+x%5BP%5D+=+-9+%2B+16+
+x%5BP%5D+=+7+
------------------
+y%5BB%5D+-+y%5BA%5D+=+-2+-+5+
+y%5BB%5D+-+y%5BA%5D+=+-7+
+4%2F1+=+y+%2F+%28+-7+-+y+%29+
+4%2A%28+-7+-+y+%29+=+y+
+-28+-+4y+=+y+
+5y+=+-28+
+y+=+-5.6+
-------------
+y%5BP%5D+=+y%5BA%5D+%2B%28+-5.6+%29+
+y%5BP%5D+=+5+-+5.6+
+y%5Bp%5D+=+-.6+
---------------------
I get P( 7, -.6 ) for the required point
Definitely get another opinion on this.
I could easily get the math wrong