Question

Triangle JKL
has vertices J(−4,−1)
, K(0,4)
, and L(−4,−2)
. Graph the triangle and its image after a dilation with a scale factor of 0.5.

Answer 1

To graph triangle JKL with vertices \( J(-4, -1) \), \( K(0, 4) \), and \( L(-4, -2) \), follow these steps:

1. **Plot the Original Triangle**:
- Point J at \((-4, -1)\)
- Point K at \((0, 4)\)
- Point L at \((-4, -2)\)

After plotting these points, connect them to form triangle JKL.

2. **Calculate the Dilation**:
The dilation of a point \( P(x, y) \) with respect to the origin \((0,0)\) using a scale factor \( k \) is given by:
\[
P'(x', y') = (k \cdot x, k \cdot y)
\]
In this case, the scale factor \( k = 0.5 \).

Let's apply the dilation to each vertex:
- For point J:
\[
J' = (0.5 \cdot -4, 0.5 \cdot -1) = (-2, -0.5)
\]

- For point K:
\[
K' = (0.5 \cdot 0, 0.5 \cdot 4) = (0, 2)
\]

- For point L:
\[
L' = (0.5 \cdot -4, 0.5 \cdot -2) = (-2, -1)
\]

3. **Plot the Dilated Triangle**:
- Point \( J'(-2, -0.5) \)
- Point \( K'(0, 2) \)
- Point \( L'(-2, -1) \)

4. **Graph the new triangle**: Connect these plotted points \( J' \), \( K' \), and \( L' \) to form the dilated triangle.

5. **Visualize** the graph with both triangles to see the scaling effect.

By following these steps, you will have a visual representation of triangle JKL and its image after dilation. If you're using graph paper or a graphing tool, ensure to label both triangles clearly to show the original and dilated versions.