look at the diagram below.$overrightarrow{jk}$ and $overrightarrow{mw}$ will be dilated by a scale factor of 1.25 centered at point $j$ to create $overrightarrow{jk}$ and $overrightarrow{mw}$, respectively.select all of the true statements.$overrightarrow{mw}$ will be parallel to $overrightarrow{mw}$, but they will not be the same line.$overrightarrow{jk}$ will be the same line as $overrightarrow{jk}$.$overrightarrow{jk}$ will be parallel to $overrightarrow{jk}$, but they will not be the same line.$overrightarrow{mw}$ will be the same line as $overrightarrow{mw}$.

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# Brief Explanations:
1. Recall the property of dilation: A dilation preserves the parallelism of lines. So, if we dilate $\overleftrightarrow{JK}$ and $\overleftrightarrow{MW}$ centered at $J$, the image of $\overleftrightarrow{JK}$ (which is $\overleftrightarrow{J'K'}$) should be the same line as $\overleftrightarrow{JK}$ because the center of dilation is on $\overleftrightarrow{JK}$, so dilating a line with a center on the line leaves the line unchanged (same line).
2. For $\overleftrightarrow{MW}$ and its image $\overleftrightarrow{M'W'}$: Since dilation preserves parallelism, $\overleftrightarrow{M'W'}$ will be parallel to $\overleftrightarrow{MW}$, but since the center of dilation is $J$ (not on $\overleftrightarrow{MW}$ initially, looking at the diagram), the image $\overleftrightarrow{M'W'}$ will not be the same line as $\overleftrightarrow{MW}$, but parallel. Wait, no, wait: Wait, the original lines $\overleftrightarrow{JK}$ and $\overleftrightarrow{MW}$ are parallel (from the diagram, they are two parallel lines). When we dilate $\overleftrightarrow{JK}$ centered at $J$, the image $\overleftrightarrow{J'K'}$ is the same line as $\overleftrightarrow{JK}$ (because the center is on the line, so dilation doesn't change the line, just the points on it). For $\overleftrightarrow{MW}$, dilating it centered at $J$ (a point not on $\overleftrightarrow{MW}$) will produce a line $\overleftrightarrow{M'W'}$ that is parallel to $\overleftrightarrow{MW}$ (since dilation preserves parallelism) but not the same line (because the center is not on $\overleftrightarrow{MW}$). Wait, but the options: Let's re - examine the options:

Option 1: $\overleftrightarrow{M'W'}$ will be parallel to $\overleftrightarrow{MW}$, but they will not be the same line. This is correct because dilation preserves parallelism, and since the center $J$ is not on $\overleftrightarrow{MW}$, the image line is parallel but distinct.

Option 2: $\overleftrightarrow{J'K'}$ will be the same line as $\overleftrightarrow{JK}$. This is correct because the center of dilation $J$ lies on $\overleftrightarrow{JK}$, so dilating a line with a center on the line results in the same line.

Option 3: $\overleftrightarrow{J'K'}$ will be parallel to $\overleftrightarrow{JK}$, but they will not be the same line. This is incorrect because, as the center is on $\overleftrightarrow{JK}$, the image line is the same as the original.

Option 4: $\overleftrightarrow{M'W'}$ will be the same line as $\overleftrightarrow{MW}$. This is incorrect because the center $J$ is not on $\overleftrightarrow{MW}$, so the dilated line is parallel but not the same.

Wait, maybe I misread the options. Let's list the options again:

1. $\overleftrightarrow{M'W'}$ will be parallel to $\overleftrightarrow{MW}$, but they will not be the same line. (Correct, because dilation preserves parallelism, and center not on $MW$ so different line but parallel)

2. $\overleftrightarrow{J'K'}$ will be the same line as $\overleftrightarrow{JK}$. (Correct, because center $J$ is on $JK$, so dilating $JK$ centered at $J$ gives the same line)

3. $\overleftrightarrow{J'K'}$ will be parallel to $\overleftrightarrow{JK}$, but they will not be the same line. (Incorrect, since center is on $JK$, it's the same line)

4. $\overleftrightarrow{M'W'}$ will be the same line as $\overleftrightarrow{MW}$. (Incorrect, as center not on $MW$, so parallel but different line)

So the true statements are: $\overleftrightarrow{J'K'}$ will be the same line as $\overleftrightarrow{JK}$ and $\overleftrightarrow{M'W'}$ will be parallel to $\overleftrightarrow{MW}$, but they will not be the same line.

# Answer:
- $\overleftrightarrow{J'K'}$ will be the same line as $\overleftrightarrow{JK}$
- $\overleftrightarrow{M'W'}$ will be parallel to $\overleftrightarrow{MW}$, but they will not be the same line

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