Question 1065525
Find the midpoints of the sides,
A(2,4)
B(2,6)
C(6,4)
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To find the midpoint, take the averages of the x and y values,
Midpoint of AC: ({{{(2+6)/2}}},{{{(4+4)/2}}})=(4,4)
Midpoint of AB: ({{{(2+2)/2}}},{{{(4+6)/2}}})=(2,5)
Midpoint of BC: ({{{(2+6)/2}}},{{{(6+4)/2}}})=(4,5)
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Now find the lines through mAC and B(line 1), mAB and C(line 2), and mBC and A(line 3).
First find the slope, then use the point slope form of a line,
I'll use the designation 1, 2, 3 for the lines as defined in the previous sentence.
Line 1:
{{{m[1]=(4-6)/(4-2)=-2/2=-1}}}
{{{y-4=-1(x-4)}}}
{{{y-4=-x+4}}}
{{{y[1]=-x+8}}}
Line 2:
{{{m[2]=(5-4)/(2-6)=1/(-4)=-1/4}}}
{{{y-5=-(1/4)(x-2)}}}
{{{y-5=-x/4+1/2}}}
{{{y=-x/4+1/2+10/2}}}
{{{y[2]=-x/4+11/2}}}
Now that we have two lines, we can calculate their intersection (which is the circumcenter),
{{{-x+8=-x/4+11/2}}}
{{{-4x+32=-x+22}}}
{{{-3x=-10}}}
{{{x[CC]=10/3}}}
and
{{{y=-10/3+8}}}
{{{y=-10/3+24/3}}}
{{{y[CC]=14/3}}}
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*[illustration af7.JPG].