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.

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.