Question 1047767
{{{m=(-2-0)/(3-4)=-2/(-1)=2}}}
{{{y-0=2(x-4)}}}
{{{y=2x-8}}}---------Equation for the line containing the two given points.



{{{sqrt((-2-0)^2+(3-4)^2)}}}
{{{sqrt(4+1)}}}
{{{sqrt(5)}}}-----------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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<i>...extended each way a distance equal to three times its own length. find the terminal points.</i>



A view of the line:
{{{graph(300,300,-7,7,-7,7,2x-8)}}}



Again use the Distance Formula, separately handling the extension of described distance from each of the given points.  Wanted is a distance of {{{1*sqrt(5)+3*sqrt(5)=highlight_green(4*sqrt(5))}}}  from a given point TOWARD AND PAST the other given point.


<u>FROM (4,0) DOWNWARD</u>
{{{sqrt((x-4)^2+(2x-8-0)^2)=4*sqrt(5)}}}
Solve for x and evaluate the corresponding y using y=2x-8.
Decide which of the two possible points is correct for the situation.


<u>FROM (3,-2) UPWARD</u>
{{{sqrt((x-3)^2+(2x-8-(-2))^2)=4*sqrt(5)}}}
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.