Question 879934
<b>Line BC</b>


{{{(0-(-2))/(4-2)=1}}}, the slope.
b=y-mx
{{{b=-2-1*2}}}
{{{b=-4}}}
{{{highlight_green(y=x-4)}}}.


<b>Length BC</b>
{{{sqrt((2-4)^2+(-2-0)^2)}}}
{{{sqrt(4+4)}}}
{{{sqrt(8)}}}
{{{highlight_green(BC=2sqrt(8))}}}


<b>Line containing A and perpendicular to line BC</b>
Want slope <b>-1</b>.
{{{Line, y-4=-1(x-1)}}}
{{{y-4=-x+1}}}
{{{highlight(y=-x-3)}}}, one of the answers.


<b>Point of intersection these two lines</b>
{{{x-4=-x-3}}}
{{{2x-4=-3}}}
{{{2x=4-3}}}
{{{2x=1}}}
{{{x=1/2}}}
-
Either equation line, y=-x-3
{{{y=-1/2-6/2}}}
{{{y=-7/2}}}
Point on line BC, containing A is <b>(1/2, -7/2)</b>.


<b>What next?</b>
Find the distance from A(1,4) to (1/2, -7/2), call the distance AP.
Find the area of the triangle ABC using {{{highlight((1/2)BC*AP)}}}.