document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1117805>Question 1117805</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the image of the point under a dilation centered at (0,0) with the given scale factor simplify completely <BR>\n" );
document.write( "(5/4,-3/2)<BR>\n" );
document.write( "scale factor=1/10 equals (/,/)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #733156 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=733156\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "By definition, the image of a point (a,b) under a dilation centered at the origin (0,0) with scale factor n is the point (na,nb).<br><BR>\n" );
document.write( "I think you should be able to figure out the answer.<br><BR>\n" );
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document.write( "Let's look at the problem with numbers that are easier to work with.<br><BR>\n" );
document.write( "In everyday usage, a dilation means something is getting bigger, as when the pupil of your eye gets larger when there is less light to allow you to see better.<br><BR>\n" );
document.write( "As used in mathematics, a dilation can make things either bigger or smaller -- by whatever the scale factor is.<br><BR>\n" );
document.write( "So a dilation with a scale factor of 3 makes thing 3 times as big; a dilation with a scale factor of 1/2 makes things half as big.<br><BR>\n" );
document.write( "When the dilation is of a point with the dilation centered at (0,0), then the distance from (0,0) to the point is multiplied by the scale factor.  Think of an arrow from (0,0) to the point; the dilation multiplies the length of the arrow by the scale factor, making it either longer or shorter.<br><BR>\n" );
document.write( "For example, for a dilation of the point (3,5) with center at (0,0) and a scale factor of 4, the image of the point will be (3*4,5*4) = (12,20).<br><BR>\n" );
document.write( "Or for a dilation of the point (-4,10) with center (0,0) and a scale factor of 1/2, the image of the point will be (-4/2,10/2) = (-2,5).<br><BR>\n" );
document.write( "The numbers in your problem are just harder to work with, because the coordinates of the given point and the scale factor are all fractions.<BR>\n" );
document.write( "The x coordinate of the image is the x coordinate of the given point, multiplied by the scale factor: (5/4) times (1/10).<BR>\n" );
document.write( "The y coordinate is the y coordinate multiplied by the scale factor: (-3/2) times (1/10).<br><BR>\n" );
document.write( "So finding the image is an exercise in multiplying and simplifying fractions.... </SPAN>\n" );
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