SOLUTION: find the trisection points of the line joining (-6,2) and (3,8).

Algebra ->  Points-lines-and-rays -> SOLUTION: find the trisection points of the line joining (-6,2) and (3,8).      Log On


   

Question 819373: find the trisection points of the line joining (-6,2) and (3,8).
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Find equation for the line:
y=mx%2Bb
b=y-mx
b=y-%28%288-2%29%2F%283-%28-6%29%29%29x
b=y-%282%2F3%29x
Pick either point: (3,8),
b=8-%282%2F3%29%2A3
b=6
Equation is y=%282%2F3%29x%2B6

Distance between the two points:
Using Distance Formula,
sqrt%28%288-2%29%5E2%2B%283-%28-6%29%29%5E2%29=sqrt%2836%2B81%29
sqrt%28117%29
3%2Asqrt%2813%29

You want a point (x,y) which is distance sqrt(13) away from (-6,2), and another point which is 2*sqrt(13) from (-6,2). Use distance formula.
Your unknown points begin as (x, (2/3)x+6 ), and you must take results for which x%3E-6 and y%3E2.
'
continuing this way,
sqrt%28%28x-%28-6%29%29%5E2%2B%282-%28%282%2F3%29x%2B6%29%29%5E2%29=sqrt%2813%29
Solve for x and find the corresponding y....