document.write( "Question 388495: 1. Kite ABCD has 2 of its vertices at A(-3,8) and B(7,14).\r
\n" ); document.write( "\n" ); document.write( "1(a). Given that the equation of the longer diagonal BD is y=4x-14, find the equation of the short diagonal AC expressing your answer in the form ax+by+c=0.\r
\n" ); document.write( "\n" ); document.write( "1(b). Find the co-ordinates of E, which is the point of intersection.\r
\n" ); document.write( "\n" ); document.write( "1(c). Hence establich the co-ordinates of C.\r
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\n" ); document.write( "\n" ); document.write( "Can you please provide solutions with full answers please.\r
\n" ); document.write( "\n" ); document.write( "Many Thanks,
\n" ); document.write( "Andy. \n" ); document.write( "
Algebra.Com's Answer #274850 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
1. Kite ABCD has 2 of its vertices at A(-3,8) and B(7,14).
\n" ); document.write( "1(a). Given that the equation of the longer diagonal BD is y=4x-14, find the equation of the short diagonal AC expressing your answer in the form ax+by+c=0.
\n" ); document.write( "1(b). Find the co-ordinates of E, which is the point of intersection.
\n" ); document.write( "1(c). Hence establich the co-ordinates of C.
\n" ); document.write( "Can you please provide solutions with full answers please.
\n" ); document.write( "Many Thanks,
\n" ); document.write( "Andy.\r
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document.write( "We just help you with the first problem. Post again for the others.\r\n" );
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document.write( "1(a). Given that the equation of the longer diagonal BD is y=4x-14, find the\r\n" );
document.write( "equation of the short diagonal AC expressing your answer in the form ax+by+c=0.\r\n" );
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document.write( "To write the equation of AC we must have its slope and a point it goes through.\r\n" );
document.write( "We already have a point it goes through, namely A(-3,8). Now all we need is it\r\n" );
document.write( "slope.  We know that AC is perpendicular to BD, and we know that to find the\r\n" );
document.write( "slope of a second line perpendicular to a first line, we invert the slope of\r\n" );
document.write( "the first line and change its sign.  \r\n" );
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document.write( "The long diagonal BD has equation y = 4x-14.  We compare that to y=mx+b\r\n" );
document.write( "and see that BD has slope m=4.  Since the short diagonal AC is perpendicular\r\n" );
document.write( "to the long diagonal BD, then AC has slope \"-1%2F4\".  Next, to find its\r\n" );
document.write( "equation we use the point-slope form: \r\n" );
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document.write( "    y - y1 = m(x - x1)\r\n" );
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document.write( "      y - 8 = \"expr%28-1%2F4%29\"[x - (-3)]\r\n" );
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document.write( "      y - 8 = \"expr%28-1%2F4%29\"(x +3)\r\n" );
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document.write( "Multiply through by 4:\r\n" );
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document.write( "    4y - 32 = -1(x + 3)\r\n" );
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document.write( "    4y - 32 = -x - 3\r\n" );
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document.write( "x + 4y - 29 = 0\r\n" );
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document.write( "That's the equation of AC in the form ax+by+c=0\r\n" );
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document.write( "1(b). Find the co-ordinates of E, which is the point of intersection.\r\n" );
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document.write( "To do that we solve the system of equations:\r\n" );
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document.write( "          y = 4x - 14\r\n" );
document.write( "x + 4y - 29 = 0\r\n" );
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document.write( "by substitution and get (x,y) = (5,6), so we can label point E as E(5,6)\r\n" );
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document.write( "1(c). Hence establich the co-ordinates of C. \r\n" );
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document.write( "To establish the coordinates of point C we realize that E(5,6) is\r\n" );
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document.write( "8 units to the right of point A(-3,8), since 5-(-3) = +8, and also\r\n" );
document.write( "that E is 2 units below point A((-3,8) since 6-9 = -2.\r\n" );
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document.write( "So therefore point C must be 8 units right and 2 units below point\r\n" );
document.write( "E(5,6).  Since 5+8=13, and 6-2 = 4, then point C must be (13,4), so\r\n" );
document.write( "we can fill in the coordinates of point C:\r\n" );
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document.write( "The kite is the red figure below, although we are not given enough information\r\n" );
document.write( "to find the coordinates of D, so we can only leave that point as just D(?,?). \r\n" );
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document.write( "Edwin
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