Question

1. consider $\triangle jkl$ and $\overrightarrow{ab}$.

a. draw and label the image of $\triangle jkl$ under the following sequence of transformations.

• dilation with center $k$ and scale factor $\frac{3}{4}$
• translation along $\overrightarrow{ab}$

b. locate the center of dilation for the single dilation that maps $\triangle jkl$ onto $\triangle jkl$. label the point $o$.
c. what is the scale factor of the dilation with center $o$ that maps $\triangle jkl$ onto $\triangle jkl$?
remember
for problems 9–12, solve for $x$.

1. $5x + 7 = 17$
2. $8x - 5 = 83$
3. $15x + 28 = -2$
4. $11x - 3 = -14$

Explanation:

For Problems 9-12:

Step1: Isolate the x-term

Subtract constants from both sides.

Step2: Solve for x

Divide by coefficient of x.

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Problem 9: $5x + 7 = 17$

Step1: Subtract 7 from both sides

$5x + 7 - 7 = 17 - 7$
$5x = 10$

Step2: Divide by 5

$x = \frac{10}{5}$

1. Dilation Step: For each vertex of $\triangle JKL$:

• $K$ stays at its original position (center of dilation).
• For $J$: Measure the distance from $K$ to $J$, multiply by $\frac{3}{4}$, mark the new point $J'$ along segment $KJ$.
• For $L$: Measure the distance from $K$ to $L$, multiply by $\frac{3}{4}$, mark the new point $L'$ along segment $KL$.
• Connect $J'$, $K$, $L'$ to get $\triangle J'KL'$.

1. Translation Step: Move each point of $\triangle J'KL'$ along the direction of $\overrightarrow{AB}$ (from $B$ to $A$, matching the length of $\overrightarrow{AB}$) to get $\triangle J''K''L''$.

Draw straight lines connecting corresponding vertices: $\overline{JJ''}$, $\overline{KK''}$, $\overline{LL''}$. The intersection point of these three lines is the center of dilation $O$.

Answer:

$x = 2$

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Problem 10: $8x - 5 = 83$

Step1: Add 5 to both sides

$8x - 5 + 5 = 83 + 5$
$8x = 88$

Step2: Divide by 8

$x = \frac{88}{8}$