Dilating Lines (Grade 9)
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Dilating Lines
1.
Line [math]\stackrel{\leftrightarrow}{AB}[/math] is dilated by a factor of [math]k[/math], where [math]k!=0,1[/math]. The center of dilation is [math](x_0,y_0)[/math], a point which does not lie on [math]\stackrel{\leftrightarrow}{AB}[/math]. Which of the following is true about [math]stackrel{leftrightarrow}{AB}[/math] and the dilated line [math]\stackrel{leftrightarrow}{A'B'} ?[/math]
- The lines are parallel, but not coincident.
- The lines are either parallel or coincident.
- The distance between the lines is k units.
- One of the lines must pass through the origin.
2.
Line [math]\stackrel{leftrightarrow}{AB}[/math] undergoes a dilation by a factor of [math]k[/math], centered at [math](x_0, y_0)[/math]. Which of the following conditions ensure(s) that [math]\stackrel{leftrightarrow}{AB}[/math] and [math]\stackrel{leftrightarrow}{A'B'}[/math], the dilated line, are coincident? Choose all correct answers.
- [math]0 < |k| < 1[/math]
- [math]k=1[/math]
- [math](x_0, y_0) = (0,0)[/math]
- [math](x_0, y_0)[/math] lies on [math]stackrel{leftrightarrow}{AB}[/math]
3.
Line [math]l[/math], with equation [math]y = 3x - 1[/math], is dilated by a factor of 3, with the center of dilation being the origin. Which of the following is the equation of the dilated line?
- [math]y = 9x - 3[/math]
- [math]y = 3x - 9[/math]
- [math]y = 3x - 3[/math]
- [math]y = x - 1/3[/math]
4.
Line [math]t[/math], with equation [math]y = -8x+6[/math], is dilated by a factor of [math]1/2[/math] with the center of dilation being the origin. What is the equation of the dilated line?
- [math]y = -4x + 6[/math]
- [math]y = -4x + 3[/math]
- [math]y = -8x + 3[/math]
- [math]y = -16x + 12[/math]
5.
Line [math]s[/math], with equation [math]y = -3x + 1/4[/math], is dilated by a factor of -4, the center of dilation being the origin. What is the equation of the dilated line?
- [math]y=3/4 x -1[/math]
- [math]y = -3x - 1[/math]
- [math]y = -3/4x + 1/4[/math]
- [math]y = 12x - 1[/math]
6.
Line [math]l[/math], with equation [math]y=-3/2x + 5[/math], is dilated by a factor of [math]1/4[/math] with the center of dilation being [math](6,1)[/math]. What is the equation of the dilated line?
- [math]y = -3/2 x + 5/4[/math]
- [math]y = -3/2 x + 2[/math]
- [math]y = -3/2 x + 35/4[/math]
- [math]y = -3/2 x - 7/4[/math]
7.
Line [math]m[/math], with equation [math]y = 1/2 x -3[/math], is dilated by a factor of 2 with the center of dilation being [math](-1,-1)[/math]. What is the equation of the dilated line?
- [math]y = 1/2 x -5[/math]
- [math]y = 1/2 x + 7/2[/math]
- [math]y = 1/2 x - 11/2[/math]
- [math]y = 1/2 x - 6[/math]
8.
Line [math]l[/math], with equation [math]y = 1/5 x - 10[/math], is dilated by factor of [math]1/5[/math] with the center of dilation being [math](5,-9)[/math]. What is the equation of the dilated line?
- [math]y = 1/5x - 10[/math]
- [math]y = 1/5x - 2[/math]
- [math]y = 1/5x - 46/5[/math]
- [math]y = 1/5 x + 146/25[/math]
9.
Line [math]s[/math] passes through the points [math]A(-3,1)[/math] and [math]B(4,4)[/math]. If line [math]s[/math] undergoes a dilation of factor 4, centered at [math](9,7)[/math], what is the equation of the dilated line?
- [math]y = 3/7x + 22/7[/math]
- [math]y = 3/7 x - 162/7[/math]
- [math]y = 1/3x + 8[/math]
- [math]y = 3/7x - 2/7[/math]
10.
Line [math]l[/math], with equation [math]y = 7x-2[/math], is dilated. The center of dilation is [math](-3,4)[/math]. If the equation of the dilated line is [math]y=7x+23/2[/math], what is the scale factor?
- [math]-9/10[/math]
- [math]1/2[/math]
- [math]-23/4[/math]
- Not enough information given.
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