Question

1. create an image by applying a dilation with point c as the center of dilation and a scale factor of 2.

1. create an image by applying a dilation with point c as the center of dilation and a scale factor of \\(\frac{1}{2}\\).

Explanation:

Step1: For Problem 2: Connect C to each vertex

Draw lines from point $C$ to each of the 3 vertices of the given triangle, extending them outward past each vertex.

Step2: For Problem 2: Extend segments to scale

For each vertex $V$, measure the distance $CV$, then mark a new point $V'$ on the extension of $CV$ such that $CV' = 2 \times CV$.

Step3: For Problem 2: Connect new vertices

Connect the three new points $V'$ to form the dilated triangle.

Step4: For Problem 3: Connect C to each vertex

Draw lines from point $C$ to each of the 3 vertices of the given triangle.

Step5: For Problem 3: Mark midpoints of segments

For each vertex $V$, mark a new point $V''$ on segment $CV$ such that $CV'' = \frac{1}{2} \times CV$ (this is the midpoint of $CV$).

Step6: For Problem 3: Connect new vertices

Connect the three new points $V''$ to form the dilated triangle.

Answer:

1. For scale factor 2 (Problem 2): A larger triangle, with all vertices twice as far from point $C$ as the original triangle's vertices, oriented the same way as the original triangle.
2. For scale factor $\frac{1}{2}$ (Problem 3): A smaller triangle, with all vertices half as far from point $C$ as the original triangle's vertices, oriented the same way as the original triangle.