Question 954683
{{{drawing(300,300,-2,10,-2,10,grid(1),
circle(0,0,0.25),
circle(9,0,0.25),
circle(7,0,0.25),
circle(9,6,0.25),
circle(0,6,0.25),
circle(5.9,0.9,0.25),
line(0,0,9,0),
line(9,0,9,6),
line(9,6,0,6),
line(0,6,0,0),
line(0,6,7,0),
line(9,6,5.9,.9))}}}
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You know that,
{{{PT^2+PS^2=ST^2}}}
{{{7^2+6^2=ST^2}}}
{{{ST^2=49+36}}}
{{{ST^2=85}}}
{{{ST=sqrt(85)}}}
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Find the line that goes through points T and S.
{{{m=(0-6)/(7-0)=-6/7}}}
{{{y-0=-(6/7)(x-7)}}}
{{{y[ST]=-(6/7)x+6}}}
The perpendicular line would have a slope that is the negative reciprocal,
{{{m[p]=7/6}}}
So the perpendicular line through R would be,
{{{y-6=(7/6)(x-9)}}}
{{{y-6=(7/6)x-21/2}}}
{{{y=(7/6)x-21/2+12/2}}}
{{{y[perp]=(7/6)x-9/2}}}
Find the point of intersection (V) using these two lines,
{{{-(6/7)x+6=(7/6)x-9/2}}}
{{{-(6/7+7/6)x=-9/2-12/2}}}
{{{-(85/42)x=-21/2}}}
{{{x=441/85}}}
Then,
{{{y=1029/170-765/170}}}
{{{y=264/170}}}
{{{y=132/85}}}
Now that you have V use the distance formula,
{{{D[RV]^2=(9-441/85)^2+(6-132/85)^2}}}
{{{D[RV]^2=(324/85)^2+(378/85)^2}}}
{{{D[RV]^2=(104976+142884)/(85)^2}}}
{{{D[RV]^2=(247860)/(85)^2}}}
{{{D[RV]^2=(2916)/(85)}}}
{{{D[RV]=sqrt(2916/85)}}}
{{{D[RV]=(54/85)sqrt(85)}}}