Question 1064783
Distance between the given points:
{{{sqrt((4-(-6))^2+(5-10)^2)}}}
{{{sqrt(125)}}}


Equation of the line containing the two given points:
slope  {{{5/(-10)}}} or slope {{{-1/2}}}.
{{{y-5=-(1/2)(x-4)}}}
{{{y-5=-x/2+2}}}
{{{y=-x/2+7}}}, 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):
{{{sqrt((x-4)^2+(-x/2+7-5)^2)=(7/10)*sqrt((-6-4)^2+(10-5)^2)}}}

.
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{{{(x-4)^2+(-x/2+2)^2=(49/100)*125}}}
{{{4(x-4)^2+(4-x)^2=245}}}
.
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{{{(x^2-8x-33)=0}}}
{{{(x+3)(x-11)=0}}}-----one of these factors will work and one of them will not.



Coordinates wanted:  {{{system(x=-3,y=8&1/2)}}}