document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1122728>Question 1122728</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Verify that P = (1, -1) is the same distance from A = (5, 1) as it is from B = (-1, 3). Find three more points that are equidistant from A and B. Can points equidistant from A and B be found in every quadrant? </SPAN>\n" );
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document.write( "The points equidistant from A and B are the points on the perpendicular bisector of segment AB.<br><BR>\n" );
document.write( "Segment AB has slope -1/3 and midpoint (2,2).<br><BR>\n" );
document.write( "The perpendicular bisector of AB has slope 3 and passes through (2,2); its equation is y = 3x-4.<br><BR>\n" );
document.write( "(a) Verify that (1,-1) is equidistant from A and B.<br><BR>\n" );
document.write( "Yes; the point (1,-1) satisfies the equation of the perpendicular bisector of AB.<br><BR>\n" );
document.write( "(b) Find three more points that are equidistant from A and B.<br><BR>\n" );
document.write( "You can do this easily; choose any values of x and use the equation of the perpendicular bisector to find the corresponding y values.<br><BR>\n" );
document.write( "(c) No.  The perpendicular bisector has slope 3 and y-intercept -4; it passes through quadrants I, III, and IV but not through quadrant II. </SPAN>\n" );
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