Expression 11: 0 less than or equal to "y" less than or equal to left parenthesis, StartFraction, StartRoot, 3 , EndRoot minus 1 Over 1 minus StartRoot, 3 , EndRoot , EndFraction , right parenthesis left parenthesis, "x" minus StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction "a" , right parenthesis plus StartFraction, "a" Over 2 , EndFraction left brace, StartFraction, "a" Over 2 , EndFraction less than "x" less than StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction "a" , right brace0≤y≤3−11−3x−32a+a2a2<x<32a
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Expression 12: 0 less than or equal to "y" less than or equal to left parenthesis, StartFraction, 1 Over StartRoot, 3 , EndRoot minus 2 , EndFraction , right parenthesis left parenthesis, "x" minus "a" , right parenthesis left brace, StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction "a" less than "x" less than "a" , right brace0≤y≤13−2x−a32a<x<a
12
Hidden Label: left parenthesis, "b" , 0 , right parenthesisb,0
Label
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The next set of equations draws the linear line that forms the triangle in the first quadrant. I made the point (0,a) to be fixated at the endpoint of the quarter circle, so the triangular region depends on the point on the horizontal axis.
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Expression 15: "m" equals negative StartFraction, "a" Over "b" , EndFractionm=−ab
equals=
negative 1.2 7 8 7 7 2 3 7 8 5 2−1.27877237852
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Expression 16: "y" equals "m" "x" plus "a"y=mx+a
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Expression 17: "b" equals 3.9 1b=3.91
00
55
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Expression 18: 0 less than or equal to "y" less than or equal to "m" "x" plus "a" left brace, 0 less than "x" less than "a" , right brace0≤y≤mx+a0<x<a
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Make sure that when adjusting the value of b, the value of a is greater than the value of b.
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Remark: You will end up obtaining 2 congruent triangular regions if the triangle is 30-60-90 or 45-45-90. This can easily be proven mathematically.
