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This printable supports Common Core Mathematics Standard HSG-SRT.A.1, HSG-SRT.A.1a

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## Dilating Lines

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