document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1127556>Question 1127556</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The coordinates of A are(-3,2) And the coordinates of C are(5,6) .The midpoint of AC is M and the perpendicular bisector of AC cuts the x-axis at B. <BR>\n" );
document.write( "Given that ABCD is a square,find the coordinates of D and the length of AD. </SPAN>\n" );
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document.write( "A(-3,2), C(5,6)  -->  midpoint M is (1,4)  [x coordinate is average of -3 and 5; y coordinate is average of 2 and 6]<br><BR>\n" );
document.write( "To find the slope of AC, I strongly recommend drawing a picture instead of plugging numbers into the slope formula.  It's very easy to get wrong numbers in the wrong places in the formula; it's easy to get the right slope using a picture.<br><BR>\n" );
document.write( "From A to C is 8 to the right and up 4; that makes the slope 4/8 = 1/2.  The slope of the perpendicular is then -2.<br><BR>\n" );
document.write( "Again use the picture to find where the perpendicular bisector crosses the x-axis, instead of plugging numbers into a formula.  The slope is -2; the midpoint M is at (1,4), 4 units above the x-axis.  If the slope is -2 and you need to go down 4 units to get to the x-axis, you need to move 2 to the right; 2 to the right from 1 is x=3.<br><BR>\n" );
document.write( "So point B is at (3,0).<br><BR>\n" );
document.write( "The problem says it is given that ABCD is a square; but it is easy to show that AB and BC are two sides of a square: A to B is 6 right and 2 down; B to C is 2 right and 6 up.  The picture shows those two segments are perpendicular, and that they have the same length of sqrt(40), or 2*sqrt(10).<br><BR>\n" );
document.write( "And to find the coordinates of D, we again use the picture.  From B to C is 2 right and 6 up; if ABCD is a square, then A to D is also 2 right and 6 up.  2 right and 6 up from A(-3,2) is (-1,8).<br><BR>\n" );
document.write( "ANSWERS: Point D is (-1,8); the length of AD is the length of either AB or BC, which is 2*sqrt(10). </SPAN>\n" );
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