Question

here is a diagram with triangle efg and point c. dilate triangle efg using center c and scale factor \\(\frac{1}{2}\\). use your cursor and digital ruler to draw on the image below.

Explanation:

Step1: Identify the center of dilation

The center of dilation is point \( C \). We need to draw lines from \( C \) through each vertex of triangle \( EFG \) (i.e., \( E \), \( F \), and \( G \)).

Step2: Determine the scale factor

The scale factor is \( \frac{1}{2} \). This means that the distance from \( C \) to each new vertex (let's call them \( E' \), \( F' \), \( G' \)) should be half the distance from \( C \) to the original vertices \( E \), \( F \), \( G \) respectively.

Step3: Locate the new vertices

• For vertex \( E \): Measure the distance from \( C \) to \( E \). Then, find a point \( E' \) on the line \( CE \) such that \( CE' = \frac{1}{2}CE \).
• For vertex \( F \): Measure the distance from \( C \) to \( F \). Then, find a point \( F' \) on the line \( CF \) such that \( CF' = \frac{1}{2}CF \).
• For vertex \( G \): Measure the distance from \( C \) to \( G \). Then, find a point \( G' \) on the line \( CG \) such that \( CG' = \frac{1}{2}CG \).

Step4: Draw the dilated triangle

Connect the new vertices \( E' \), \( F' \), and \( G' \) to form the dilated triangle \( E'F'G' \).

(Note: Since this is a drawing task, the actual drawing would involve using the digital ruler to measure the distances and mark the new points. The key steps are identifying the center, applying the scale factor to the distances from the center to each vertex, and then connecting the new vertices.)

Answer:

To dilate triangle \( EFG \) with center \( C \) and scale factor \( \frac{1}{2} \):

1. Draw lines from \( C \) through \( E \), \( F \), and \( G \).
2. On each line, mark a point (e.g., \( E' \), \( F' \), \( G' \)) halfway between \( C \) and the original vertex (since the scale factor is \( \frac{1}{2} \)).
3. Connect \( E' \), \( F' \), and \( G' \) to form the dilated triangle.

(The final answer is the drawn triangle \( E'F'G' \) as per the above steps.)