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Properties of Dilations: Mastery Test
Rectangle [tex][tex]$ABCD$[/tex][/tex] is dilated by a scale factor of 2 with the origin as the center of dilation, resulting in the image [tex][tex]$A^{\prime}B^{\prime}C^{\prime}D^{\prime}$[/tex][/tex]. If the slope of [tex][tex]$\overline{AB}$[/tex][/tex] is -2, what is the slope of [tex][tex]$\overline{A^{\prime}B^{\prime}}$[/tex][/tex]?
To find the slope of [tex]$\overline{A^{\prime} B^{\prime}}$[/tex], we need to consider the properties of dilation.
Dilation is a transformation that resizes an object by a scale factor, but it does not change the angles or the ratios of the distances between points. This means that parallel lines remain parallel and the slopes of lines remain the same before and after the dilation.
In this particular problem, the original slope of [tex]$\overline{A B}$[/tex] is given as -2. Since the dilation will not change the slope of the line:
- The slope of the original line [tex]$\overline{A B}$[/tex] is -2. - The slope of the dilated line [tex]$\overline{A^{\prime} B^{\prime}}$[/tex] will therefore also be -2.
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