https://file.aiquickdraw.com/mathbot/file/1727441535731rr8wd7ek.jpg

To solve the problem of dilating the vertices of the triangle by a scale factor of \( \frac{1}{2} \) centered at the origin, let's follow the steps:

### Step 1: Identify the Coordinates of the Original Vertices
The vertices of the triangle are labeled as \( A \), \( B \), and \( C \). From the graph, the coordinates appear to be:

- \( A (-6, -6) \)
- \( B (0, -6) \)
- \( C (-6, -10) \)

### Step 2: Apply the Dilation Formula
The dilation formula for a point \( (x, y) \) with a scale factor \( k \) centered at the origin is:

\[
(x', y') = (k \cdot x, k \cdot y)
\]

Here, the scale factor \( k = \frac{1}{2} \).

### Step 3: Calculate the New Coordinates
- For \( A (-6, -6) \):

\[
A' = \left( \frac{1}{2} \cdot (-6), \frac{1}{2} \cdot (-6) \right) = (-3, -3)
\]

- For \( B (0, -6) \):

\[
B' = \left( \frac{1}{2} \cdot 0, \frac{1}{2} \cdot (-6) \right) = (0, -3)
\]

- For \( C (-6, -10) \):

\[
C' = \left( \frac{1}{2} \cdot (-6), \frac{1}{2} \cdot (-10) \right) = (-3, -5)
\]

### Step 4: New Coordinates of the Dilated Vertices
- \( A' = (-3, -3) \)
- \( B' = (0, -3) \)
- \( C' = (-3, -5) \)

These are the coordinates of the vertices after dilation with a scale factor of \( \frac{1}{2} \).

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Would you like further details or clarifications on this solution?

### Related Questions:
1. How do you find the image of a point under dilation with a different scale factor?
2. What is the effect of dilation on the area of a triangle?
3. How would the result change if the dilation was centered at a different point?
4. Can dilation change the orientation of a figure?
5. How would a dilation with a scale factor greater than 1 affect the coordinates?

**Tip:** When dilating around the origin, multiplying each coordinate by the scale factor is all that’s needed!

Write the coordinates of the vertices after a dilation with a scale factor of 1/2 centered at the origin.

Learn how to apply dilation to a triangle with vertices A(-6, -6), B(0, -6), and C(-6, -10), using a scale factor of 1/2 centered at the origin. Step-by-step solution provided, suitable for students in Grades 8-10.

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