SOLUTION: In what ratio does the line segment joining x-y-2=0 divide the line segment (3,-1)and((8,9)

In what ratio does the line segment joining x-y-2=0 divide the line segment (3,-1)and((8,9)



Find the equation of the segment using the slope formula and
the point-slope form.  You'll get y = 2x-7

Use either substitution or elimination to solve the system
of equations


to find the point where they intersect, which you'll find 
to be (5,3).

Then use the distance formula to find the distance 

from (3,-1) to (5,3).  You'll get 

Then use the distance formula again to find the distance
from (5,3) to (8,9).  You'll get 

Then find the ratio by dividing those.  Get 2/3 if you
divide the first by the second, or 3/2 if you divide the
second by the first. Interpret the fraction as a ratio
by "NUMERATOR to DENOMINATOR".

So you can give the answer as the ratio "2 to 3" or "3 to 2",
since you weren't told which way to give the ratio when
comparing the distances, whether "smaller to larger" or
"larger to smaller".  I'd give "2 to 3" since they mention
the lower point first.

Edwin