SOLUTION: find the point which is 7/10 of the way from the point (4,5) to the point (-6,10).

Algebra ->  Length-and-distance -> SOLUTION: find the point which is 7/10 of the way from the point (4,5) to the point (-6,10).      Log On


   

Question 1064783: find the point which is 7/10 of the way from the point (4,5) to the point (-6,10).
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Distance between the given points:
sqrt%28%284-%28-6%29%29%5E2%2B%285-10%29%5E2%29
sqrt%28125%29

Equation of the line containing the two given points:
slope 5%2F%28-10%29 or slope -1%2F2.
y-5=-%281%2F2%29%28x-4%29
y-5=-x%2F2%2B2
y=-x%2F2%2B7, same as variable point (x, -x/2+7).

Point (x,y), 7/10 of the way from the point (4,5) to the point (-6,10):

.
.
%28x-4%29%5E2%2B%28-x%2F2%2B2%29%5E2=%2849%2F100%29%2A125
4%28x-4%29%5E2%2B%284-x%29%5E2=245
.
.
%28x%5E2-8x-33%29=0
%28x%2B3%29%28x-11%29=0-----one of these factors will work and one of them will not.


Coordinates wanted: system%28x=-3%2Cy=8%261%2F2%29