document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210148>Question 1210148</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three unit squares and two line segments connecting two pairs of vertices are shown. What is the area of triangle ABC?\r<BR>\n" );
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document.write( "A is at (0,0), B is at (1,0), and C is at (1,1). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851370 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=851370\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the coordinates of the vertices be $A=(0,0)$, $B=(1,0)$, and $C=(1,1)$.<BR>\n" );
document.write( "We need to find the area of triangle $ABC$.\r<BR>\n" );
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document.write( "The coordinates of the vertices are given as $A=(0,0)$, $B=(1,0)$, and $C=(1,1)$.\r<BR>\n" );
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document.write( "We can use the formula for the area of a triangle given the coordinates of its vertices:<BR>\n" );
document.write( "Area = $\frac{1}{2} |x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2)|$<BR>\n" );
document.write( "where $(x_1, y_1) = (0, 0)$, $(x_2, y_2) = (1, 0)$, and $(x_3, y_3) = (1, 1)$.\r<BR>\n" );
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document.write( "Area = $\frac{1}{2} |0(0-1) + 1(1-0) + 1(0-0)|$<BR>\n" );
document.write( "Area = $\frac{1}{2} |0 + 1 + 0|$<BR>\n" );
document.write( "Area = $\frac{1}{2} |1|$<BR>\n" );
document.write( "Area = $\frac{1}{2}$\r<BR>\n" );
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document.write( "Alternatively, we can notice that the triangle $ABC$ is a right triangle with base $AB$ and height $BC$.<BR>\n" );
document.write( "The length of $AB$ is $1-0 = 1$.<BR>\n" );
document.write( "The length of $BC$ is $1-0 = 1$.<BR>\n" );
document.write( "The area of a triangle is $\frac{1}{2} \times \text{base} \times \text{height}$.<BR>\n" );
document.write( "Area = $\frac{1}{2} \times 1 \times 1 = \frac{1}{2}$.\r<BR>\n" );
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document.write( "Final Answer: The final answer is $\boxed{\frac{1}{2}}$<BR>\n" );
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