Question 1048893
53. Determining a Line Segment with Given Midpoint Let (4, 4) be the midpoint of the line segment determined by the points (1, 2) and (a, b). Determine a and b.  



{{{(1+a)/2=4}}}
{{{1+a=8}}}
{{{a=8-1}}}
{{{a=7}}}
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{{{(2+b)/2=4}}}
{{{2+b=8}}}
{{{b=8-2}}}
{{{b=6}}}
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The unknown point is  (7,6).



54. Writing to Learn Isosceles but Not Equilateral Triangle Prove that the triangle determined by the points (3, 0), (1, 2), and (5, 4) is isosceles but not equilateral.


The three lengths of this triangle are
{{{system(sqrt((3-1)^2+(0-2)^2),sqrt((1-5)^2+(2-4)^2),sqrt((5-3)^2+(4-0)^2))}}}
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{{{system(sqrt(8),sqrt(20),sqrt(20))}}}
Exactly two of the sides are of equal length, and the other side is different length.  You need to have exactly two equal side lengths so this fits being isosceles triangle.