SOLUTION: the segment joining (4 0) and (3 -2) is extended each way a distance equal to three times its own length. find the terminal points. illustration pls.

Algebra ->  Points-lines-and-rays -> SOLUTION: the segment joining (4 0) and (3 -2) is extended each way a distance equal to three times its own length. find the terminal points. illustration pls.      Log On


   

Question 1047767: the segment joining (4 0) and (3 -2) is extended each way a distance equal to three times its own length. find the terminal points. illustration pls.
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
m=%28-2-0%29%2F%283-4%29=-2%2F%28-1%29=2
y-0=2%28x-4%29
y=2x-8---------Equation for the line containing the two given points.


sqrt%28%28-2-0%29%5E2%2B%283-4%29%5E2%29
sqrt%284%2B1%29
sqrt%285%29-----------Length of the segment joining the two given points.


Other points on the line would take a form, (x, 2x-8).

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...extended each way a distance equal to three times its own length. find the terminal points.


A view of the line:
graph%28300%2C300%2C-7%2C7%2C-7%2C7%2C2x-8%29


Again use the Distance Formula, separately handling the extension of described distance from each of the given points. Wanted is a distance of 1%2Asqrt%285%29%2B3%2Asqrt%285%29=highlight_green%284%2Asqrt%285%29%29 from a given point TOWARD AND PAST the other given point.

FROM (4,0) DOWNWARD
sqrt%28%28x-4%29%5E2%2B%282x-8-0%29%5E2%29=4%2Asqrt%285%29
Solve for x and evaluate the corresponding y using y=2x-8.
Decide which of the two possible points is correct for the situation.

FROM (3,-2) UPWARD
sqrt%28%28x-3%29%5E2%2B%282x-8-%28-2%29%29%5E2%29=4%2Asqrt%285%29
Solve for x and evaluate the corresponding y using y=2x-8.
Decide which of the two possible points is correct for the situation.


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Read the plan, and think, and when you understand it, do the steps and finish.