Question 317610
For the distance problems, use the distance formula,
{{{D^2=(x1-x2)^2+(y1-y2)^2}}}
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For the midpoint problems, use the midpoint formula,
{{{xm=(x1+x2)/2}}}
{{{ym=(y1+y2)/2}}}
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Solution for the point on the x-axis that is equal distance from (8,4) and (-4,2) 
A point on the x-axis has the form, (x,0).
{{{D1^2=(x-8)^2+(4-0)^2}}}
{{{D2^2=(x+4)^2+(2-0)^2}}}
If they're equidistant, {{{ D1=D2}}}, {{{D1^2=D2^2}}}
{{{(x-8)^2+(4)^2=(x+4)^2+(2)^2}}}
{{{x^2-16x+64+16=x^2+8x+16+4}}}
{{{x^2-16x+80=x^2+8x+20}}}
{{{-24x=-60}}}
{{{x=60/24=5/2}}}
{{{highlight(x=5/2)}}}
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Solution for the distance between the points (8,2) and (16,2)= {{{ 8 }}}
Solution for the distance between the points (2,6) and (12,8)={{{2sqrt(26)}}}
Solution for the midpoint between (8,2) and (10,6) =({{{9}}},{{{4}}})
Solution for the midpoint between (-4,2) and (-5,3)=({{{-4.5}}},{{{2,5}}})