https://file.aiquickdraw.com/mathbot/file/1727288421168i7ab5rhk.jpg

The problem asks for the coordinates of the vertices of a triangle after it undergoes a dilation with a given scale factor \( k = 0.5 \). The original vertices of the triangle are:

- \( J(-8, 0) \)
- \( K(-4, 4) \)
- \( L(-2, 0) \)

### Step-by-step solution:

To find the coordinates of the vertices after dilation, we multiply each coordinate by the scale factor \( k = 0.5 \).

#### Vertex \( J(-8, 0) \):
\[
J' = (-8 \times 0.5, 0 \times 0.5) = (-4, 0)
\]

#### Vertex \( K(-4, 4) \):
\[
K' = (-4 \times 0.5, 4 \times 0.5) = (-2, 2)
\]

#### Vertex \( L(-2, 0) \):
\[
L' = (-2 \times 0.5, 0 \times 0.5) = (-1, 0)
\]

### The new coordinates after dilation are:

- \( J'(-4, 0) \)
- \( K'(-2, 2) \)
- \( L'(-1, 0) \)

You can now graph both the original triangle \( JKL \) and the dilated triangle \( J'K'L' \) on a separate sheet of paper.

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Would you like more details on how dilation works or help with graphing?

Here are 5 questions to expand on this topic:
1. What is the general formula for dilation of coordinates?
2. How would the dilation change if the scale factor was \( k > 1 \)?
3. How do dilations affect the perimeter and area of a shape?
4. Can dilations move the shape outside the original coordinate plane?
5. What happens to the orientation of the shape after a dilation with a negative scale factor?

**Tip:** When performing dilations, the scale factor \( k \) determines how the size of the shape changes relative to the origin. If \( k \) is between 0 and 1, the shape contracts.

For the set of triangle vertices, find the coordinates of the vertices of the image after a dilation of the triangle by the given scale factor. Then graph the preimage and image on a separate sheet of paper. J(-8, 0), K(-4, 4), L(-2, 0), k = 0.5

Learn how to dilate a triangle with vertices J(-8, 0), K(-4, 4), and L(-2, 0) by a scale factor of k = 0.5. This problem covers geometric transformations and dilation techniques. Suitable for students in Grades 7-10.

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