SOLUTION: a) Find the coordinates of the point P, which divides the line joining the points, A(-10,35) and B(5,55) in the ration 3:2. b) Find the lengths of AP and PB. Thank you so much

Algebra ->  Linear-equations -> SOLUTION: a) Find the coordinates of the point P, which divides the line joining the points, A(-10,35) and B(5,55) in the ration 3:2. b) Find the lengths of AP and PB. Thank you so much       Log On


   

Question 1128593: a) Find the coordinates of the point P, which divides the line joining the points, A(-10,35) and B(5,55) in the ration 3:2.
b) Find the lengths of AP and PB.
Thank you so much :D
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+B%5Bx%5D+-+A%5Bx%5D+=+5+-%28-10%29+
+B%5Bx%5D+-+A%5Bx%5D+=+15+
+%283%2F5%29%2A15+=+9+
+-10+%2B+9+=+-1+
+P%5Bx%5D+=+-1+
-----------------------------
+B%5By%5D+-+A%5By%5D+=+55+-+35+
+B%5By%5D+-+A%5By%5D+=+20+
+%283%2F5%29%2A20+=+12+
+35+%2B+12+=+47+
+P%5By%5D+=+47+
-----------------------------
A( -10, 35 ) P( -1, 47 ) =
+sqrt%28+%28+-1+-%28-10%29+%29%5E2+%2B+%28+47+-+35+%29%5E2+%29+
+sqrt%28+9%5E2+%2B+12%5E2+%29+
+sqrt%28+81+%2B+144+%29+
+sqrt%28+225+%29+=+15+
-----------------------------
P( -1, 47 ) B( 5,55 ) =
+sqrt%28+5+-%28-1%29+%29%5E2+%2B+%28+55+-+47+%29%5E2+%29+
+sqrt%28+6%5E2+%2B+8%5E2+%29+
+sqrt%28+36+%2B+64+%29+
+sqrt%28+100+%29+=+10+
------------------------------
AP = 15
PB = 10
-----------------
check answer:
AB =
+sqrt%28+%28+55+-+35+%29%5E2+%2B+%28+5+-%28-10%29+%29%5E2+%29+
+sqrt%28+20%5E2+%2B+15%5E2+%29+
+sqrt%28+625+%29+=+25+
AB = 25
OK