SOLUTION: Find the ratio in which the line x+y=2 divides the line formed by the coordinates (-1,1) and (6,8). Please show me the working too.

Algebra ->  Formulas -> SOLUTION: Find the ratio in which the line x+y=2 divides the line formed by the coordinates (-1,1) and (6,8). Please show me the working too.       Log On


   

Question 896694: Find the ratio in which the line x+y=2 divides the line formed by the coordinates (-1,1) and (6,8).
Please show me the working too.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Find equation:
(-1,1) and (6,8)
+y+=+m%2Ax+%2B+b+
+1+=+m%2A%28-1%29+%2B+b+
+8+=+m%2A6+%2B+b+
--------------------
+6m+%2B+b+=+8+
+-m+%2B+b+=+1+
-----------------
Subtract
+6m+%2B+b+=+8+
+m+-+b+=+-1+
+7m+=+7+
+m+=+1+
and
+-m+%2B+b+=+1+
+-1+%2B+b+=+1+
+b+=+2+
-----------------
The equation is:
+y+=+x+%2B+2+
---------------
The given equation is:
+x+%2B+y+=+2+
+y+=+-x+%2B+2+
-----------------
Find the intersection of the lines
+y+=+x+%2B+2+
+y+=+-x+%2B+2+
--------------
+2y+=+4+
+y+=+2+
and
+y+=+x+%2B+2+
+2+=+x+%2B+2+
+x+=+0+
The intersection is: ( 0,2 )
-------------------------
Name: C (0,2)
Name: A (-1,1 )
Name B (6,8)
---------------
For just the x-co-ordinates:
AC/CB = +%28+-1+-+0+%29+%2F+%28+0+-+6+%29+
AC/CB = +%28-1%29%2F%28-6%29+
AC/CB = +1%2F6+
-------------------
For the y-co-ordinates:
AC/CB = +%28+1+-+2+%29+%2F+%28+2+-+8+%29+
AC/CB = +%28-1%29%2F%28-6%29+
AC/CB = +1%2F6+
-------------------
The given line is divided in x and y
by the same ratio ( as it should ), so
the line is divided in the ratio 1/6
------------------------------
Here's the plot of the lines:
+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+x%2B2%2C+-x%2B2+%29+