document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1090577>Question 1090577</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A triangle field ABC is such that AB=90 m, BC=70 m & AC=85 m. Make a scale drawing of it, using a scale of 1 cm to 10 m. From your scale drawing, find <BR>\n" );
document.write( "(a) the actual distance from A to the midpoint of BC and, <BR>\n" );
document.write( "(b) the actual distance from B to the midpoint of AC. </SPAN>\n" );
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document.write( "Not sure how you get actual distances from a scale drawing.<BR>\n" );
document.write( "You can get an estimate of the distances.<BR>\n" );
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document.write( "I'm solving it algebraically.<BR>\n" );
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document.write( "So let's set up a coordinate system with (0,0) at A.<BR>\n" );
document.write( "So then B is (90,0).<BR>\n" );
document.write( "Angle A is 47.1.<BR>\n" );
document.write( "Angle B is 62.7.<BR>\n" );
document.write( "Angle C is 70.2.<BR>\n" );
document.write( "So then the coordinates of C is <BR>\n" );
document.write( "C:(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=85cos%2847.1%29 ALIGN=MIDDLE  ALT=\"85cos%2847.1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=85sin%2847.1%29 ALIGN=MIDDLE  ALT=\"85sin%2847.1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "C:(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=57.86 ALIGN=MIDDLE  ALT=\"57.86\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=62.27 ALIGN=MIDDLE  ALT=\"62.27\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "The midpoint of AC would then be half of those values.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M%5BAC%5D ALIGN=MIDDLE  ALT=\"M%5BAC%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28.9 ALIGN=MIDDLE  ALT=\"28.9\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=31.2 ALIGN=MIDDLE  ALT=\"31.2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "So then using the distance formula.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%7B1%5D%5E2=%2890-28.9%29%5E2%2B%280-31.2%29%5E2 ALIGN=MIDDLE  ALT=\"D%7B1%5D%5E2=%2890-28.9%29%5E2%2B%280-31.2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B1%5D ALIGN=MIDDLE  ALT=\"D%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The midpoint of BC is calculated using the points B and C.<BR>\n" );
document.write( "It's the average of the x and y values.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M%5BBCx%5D=%2890%2B57.86%29%2F2=73.9 ALIGN=MIDDLE  ALT=\"M%5BBCx%5D=%2890%2B57.86%29%2F2=73.9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M%5BBCy%5D=%280%2B62.27%29%2F2=31.2 ALIGN=MIDDLE  ALT=\"M%5BBCy%5D=%280%2B62.27%29%2F2=31.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M%5BBC%5D ALIGN=MIDDLE  ALT=\"M%5BBC%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=73.9 ALIGN=MIDDLE  ALT=\"73.9\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=31.2 ALIGN=MIDDLE  ALT=\"31.2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "Again use the distance formula,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B2%5D%5E2=%280-73.9%29%5E2%2B%280-31.2%29%5E2 ALIGN=MIDDLE  ALT=\"D%5B2%5D%5E2=%280-73.9%29%5E2%2B%280-31.2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B2%5D ALIGN=MIDDLE  ALT=\"D%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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