Dilations Change Length by Scale Factor - Geometry
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What is the scale factor $k$ if a segment is reduced to one fifth of its original length?
What is the scale factor $k$ if a segment is reduced to one fifth of its original length?
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$k=\frac{1}{5}$. One fifth means multiply by $\frac{1}{5}$.
$k=\frac{1}{5}$. One fifth means multiply by $\frac{1}{5}$.
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What is the scale factor $k$ if a segment is halved in length by a dilation?
What is the scale factor $k$ if a segment is halved in length by a dilation?
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$k=\frac{1}{2}$. Halving means multiplying by $\frac{1}{2}$.
$k=\frac{1}{2}$. Halving means multiplying by $\frac{1}{2}$.
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What is the scale factor $k$ if a segment is tripled in length by a dilation?
What is the scale factor $k$ if a segment is tripled in length by a dilation?
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$k=3$. Tripling means multiplying by 3.
$k=3$. Tripling means multiplying by 3.
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Identify the correct inequality if $k=\frac{7}{4}$ and $L>0$ for a dilated segment length $L'$.
Identify the correct inequality if $k=\frac{7}{4}$ and $L>0$ for a dilated segment length $L'$.
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$L'>L$. Since $k=\frac{7}{4}>1$, the image is longer.
$L'>L$. Since $k=\frac{7}{4}>1$, the image is longer.
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Identify the correct inequality if $k=\frac{5}{6}$ and $L>0$ for a dilated segment length $L'$.
Identify the correct inequality if $k=\frac{5}{6}$ and $L>0$ for a dilated segment length $L'$.
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$L'<L$. Since $k=\frac{5}{6}<1$, the image is shorter.
$L'<L$. Since $k=\frac{5}{6}<1$, the image is shorter.
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What is the scale factor $k$ if $L=25$ and $L'=30$ under dilation?
What is the scale factor $k$ if $L=25$ and $L'=30$ under dilation?
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$k=1.2$. Scale factor is $k=\frac{30}{25}=1.2$.
$k=1.2$. Scale factor is $k=\frac{30}{25}=1.2$.
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Identify the scale factor $k$ if the statement “image length : preimage length $=3:5$” is true.
Identify the scale factor $k$ if the statement “image length : preimage length $=3:5$” is true.
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$k=\frac{3}{5}$. The ratio $3:5$ means $k=\frac{3}{5}$.
$k=\frac{3}{5}$. The ratio $3:5$ means $k=\frac{3}{5}$.
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What is the scale factor $k$ if $L=7$ and $L'=\frac{21}{2}$?
What is the scale factor $k$ if $L=7$ and $L'=\frac{21}{2}$?
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$k=\frac{3}{2}$. Scale factor is $k=\frac{\frac{21}{2}}{7}=\frac{3}{2}$.
$k=\frac{3}{2}$. Scale factor is $k=\frac{\frac{21}{2}}{7}=\frac{3}{2}$.
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What is the image length $L'$ if $L=50$ and the scale factor is $k=0.02$?
What is the image length $L'$ if $L=50$ and the scale factor is $k=0.02$?
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$L'=1$. Using $L'=kL$: $L'=50 \times 0.02=1$.
$L'=1$. Using $L'=kL$: $L'=50 \times 0.02=1$.
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Find the missing value: if $L'=kL$, $k=\frac{2}{5}$, and $L'=8$, what is $L$?
Find the missing value: if $L'=kL$, $k=\frac{2}{5}$, and $L'=8$, what is $L$?
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$L=20$. From $L'=kL$: $L=\frac{8}{\frac{2}{5}}=20$.
$L=20$. From $L'=kL$: $L=\frac{8}{\frac{2}{5}}=20$.
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Identify whether the dilation is an enlargement or reduction if the scale factor is $k=\frac{11}{10}$.
Identify whether the dilation is an enlargement or reduction if the scale factor is $k=\frac{11}{10}$.
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Enlargement. Since $k=\frac{11}{10}>1$, it's an enlargement.
Enlargement. Since $k=\frac{11}{10}>1$, it's an enlargement.
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What is the image length $L'$ if $L=9$ and the scale factor is $k=\frac{2}{3}$?
What is the image length $L'$ if $L=9$ and the scale factor is $k=\frac{2}{3}$?
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$L'=6$. Using $L'=kL$: $L'=9 \times \frac{2}{3}=6$.
$L'=6$. Using $L'=kL$: $L'=9 \times \frac{2}{3}=6$.
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What is the image length $L'$ if $L=\frac{5}{2}$ and the scale factor is $k=4$?
What is the image length $L'$ if $L=\frac{5}{2}$ and the scale factor is $k=4$?
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$L'=10$. Using $L'=kL$: $L'=\frac{5}{2} \times 4=10$.
$L'=10$. Using $L'=kL$: $L'=\frac{5}{2} \times 4=10$.
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What is the original length $L$ if the image length is $L'=9$ and $k=\frac{3}{4}$?
What is the original length $L$ if the image length is $L'=9$ and $k=\frac{3}{4}$?
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$L=12$. From $L'=kL$: $L=\frac{9}{\frac{3}{4}}=12$.
$L=12$. From $L'=kL$: $L=\frac{9}{\frac{3}{4}}=12$.
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What is the original length $L$ if the image length is $L'=14$ and $k=2$?
What is the original length $L$ if the image length is $L'=14$ and $k=2$?
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$L=7$. From $L'=kL$: $L=\frac{L'}{k}=\frac{14}{2}=7$.
$L=7$. From $L'=kL$: $L=\frac{L'}{k}=\frac{14}{2}=7$.
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What is the scale factor $k$ if a segment changes from $30$ to $24$ under dilation?
What is the scale factor $k$ if a segment changes from $30$ to $24$ under dilation?
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$k=0.8$. Scale factor is $k=\frac{24}{30}=0.8$.
$k=0.8$. Scale factor is $k=\frac{24}{30}=0.8$.
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What is the scale factor $k$ if a segment changes from $12$ to $18$ under dilation?
What is the scale factor $k$ if a segment changes from $12$ to $18$ under dilation?
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$k=\frac{3}{2}$. Scale factor is $k=\frac{18}{12}=\frac{3}{2}$.
$k=\frac{3}{2}$. Scale factor is $k=\frac{18}{12}=\frac{3}{2}$.
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What is the image length $L'$ if $L=20$ and the scale factor is $k=\frac{1}{4}$?
What is the image length $L'$ if $L=20$ and the scale factor is $k=\frac{1}{4}$?
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$L'=5$. Using $L'=kL$: $L'=20 \times \frac{1}{4}=5$.
$L'=5$. Using $L'=kL$: $L'=20 \times \frac{1}{4}=5$.
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What is the image length $L'$ if $L=15$ and the scale factor is $k=0.6$?
What is the image length $L'$ if $L=15$ and the scale factor is $k=0.6$?
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$L'=9$. Using $L'=kL$: $L'=15 \times 0.6=9$.
$L'=9$. Using $L'=kL$: $L'=15 \times 0.6=9$.
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What is the image length $L'$ if $L=8$ and the scale factor is $k=\frac{3}{2}$?
What is the image length $L'$ if $L=8$ and the scale factor is $k=\frac{3}{2}$?
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$L'=12$. Using $L'=kL$: $L'=8 \times \frac{3}{2}=12$.
$L'=12$. Using $L'=kL$: $L'=8 \times \frac{3}{2}=12$.
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Identify whether the dilation is an enlargement or reduction if the scale factor is $k=\frac{9}{10}$.
Identify whether the dilation is an enlargement or reduction if the scale factor is $k=\frac{9}{10}$.
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Reduction. Since $k=\frac{9}{10}<1$, it's a reduction.
Reduction. Since $k=\frac{9}{10}<1$, it's a reduction.
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Find and correct the error: “Under dilation, $L'=L+k$.” What is the correct relationship?
Find and correct the error: “Under dilation, $L'=L+k$.” What is the correct relationship?
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Correct: $L'=kL$. Dilation multiplies length, not adds to it.
Correct: $L'=kL$. Dilation multiplies length, not adds to it.
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Find and correct the error: “Scale factor $k=\frac{L}{L'}$.” What is the correct formula for $k$?
Find and correct the error: “Scale factor $k=\frac{L}{L'}$.” What is the correct formula for $k$?
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Correct: $k=\frac{L'}{L}$. Scale factor is image divided by original length.
Correct: $k=\frac{L'}{L}$. Scale factor is image divided by original length.
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What is the image length $L'$ if $L=13$ and the scale factor is $k=2$?
What is the image length $L'$ if $L=13$ and the scale factor is $k=2$?
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$L'=26$. Using $L'=kL$: $L'=13 \times 2=26$.
$L'=26$. Using $L'=kL$: $L'=13 \times 2=26$.
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What is the image length $L'$ if $L=13$ and the scale factor is $k=\frac{1}{2}$?
What is the image length $L'$ if $L=13$ and the scale factor is $k=\frac{1}{2}$?
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$L'=6.5$. Using $L'=kL$: $L'=13 \times \frac{1}{2}=6.5$.
$L'=6.5$. Using $L'=kL$: $L'=13 \times \frac{1}{2}=6.5$.
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What is the scale factor $k$ if a dilation decreases every length by $10%$?
What is the scale factor $k$ if a dilation decreases every length by $10%$?
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$k=0.9$. 10% decrease means keeping 90%, so $k=0.9$.
$k=0.9$. 10% decrease means keeping 90%, so $k=0.9$.
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What is the scale factor $k$ if a dilation increases every length by $10%$?
What is the scale factor $k$ if a dilation increases every length by $10%$?
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$k=1.1$. 10% increase means 110% of original, so $k=1.1$.
$k=1.1$. 10% increase means 110% of original, so $k=1.1$.
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What is the scale factor $k$ if a segment of length $0.8$ dilates to length $2.4$?
What is the scale factor $k$ if a segment of length $0.8$ dilates to length $2.4$?
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$k=3$. Scale factor is $k=\frac{2.4}{0.8}=3$.
$k=3$. Scale factor is $k=\frac{2.4}{0.8}=3$.
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Find the missing value: if $L'=kL$, $L=12$, and $L'=15$, what is $k$?
Find the missing value: if $L'=kL$, $L=12$, and $L'=15$, what is $k$?
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$k=\frac{5}{4}$. From $L'=kL$: $k=\frac{15}{12}=\frac{5}{4}$.
$k=\frac{5}{4}$. From $L'=kL$: $k=\frac{15}{12}=\frac{5}{4}$.
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What is the image length $L'$ if $L=11$ and the scale factor is $k=1.2$?
What is the image length $L'$ if $L=11$ and the scale factor is $k=1.2$?
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$L'=13.2$. Using $L'=kL$: $L'=11 \times 1.2=13.2$.
$L'=13.2$. Using $L'=kL$: $L'=11 \times 1.2=13.2$.
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