Question 957774
{{{drawing(300,300,-2,8,-6,4,grid(1),line(5,3,4,-3),line(4,-3,-1,2),line(-1,2,5,3))}}}

Use the distance formula,
{{{D[AB]^2=(4-5)^2+(-3-3)^2}}}
{{{D[AB]^2=(-1)^2+(-6)^2}}}
{{{D[AB]^2=1+36}}}
{{{D[AB]^2=37}}}
{{{D[AB]^2=sqrt(37)}}}
.
.
.
{{{drawing(300,300,-2,10,-2,10,grid(1),line(2,3,6,9),line(6,9,2,1),line(2,1,2,3))}}}
From the graph, you can tell that the base of the triangle is,
{{{b=2}}}
and the height of the triangle is 
{{{h=4}}}
So,
{{{A=(1/2)bh}}}
{{{A=(1/2)(2)(4)}}}
{{{A=4}}}
.
.
.
You can find the shortest distance by finding a perpendicular line going through (3,-5).
{{{5x=12y+26}}}
{{{12y=5x-26}}}
{{{y=(5/12)x-13/6}}}
Perpendicular line have slopes that are negative reciprocals.
{{{y-(-5)=-(12/5)(x-3)}}}
{{{y+5=-(12/5)x+36/5}}}
{{{y=-(12/5)x+11/5}}}
Find the point of intersection between the two lines.
Then find the distance between the intersection point and (3,-5).
{{{(5/12)x-13/6=-(12/5)x+11/5}}}
{{{25x-130=-144x+132}}}
{{{169x=262}}}
{{{x=262/169}}}
So then,
{{{y=(5/12)(262/169)-13/6}}}
{{{y=655/1014-2197/1014}}}
{{{y=-1542/1014}}}
{{{y=-257/169}}}
So then the distance is,
{{{D^2=(3-262/169)^2+(-5-(-257/169))^2}}}
{{{D^2=(245/169)^2+(-588/169)^2}}}
{{{D^2=(60025)/169^2+(345744)/169^2}}}
{{{D^2=(405769)/169^2}}}
{{{D^2=(637)^2/169^2}}}
{{{D=637/169}}}
.
.
.
{{{drawing(300,300,-2,8,-8,2,grid(1),
circle(3,-5,0.2),
circle(262/169,-257/169,0.2),

blue(line(3,-5,262/169,-257/169)),
graph(300,300,-2,8,-8,2,(5/12)x-26/12,-(12/5)x+11/5)))}}}