Question

draw the image of the following triangle after a dilation centered at the origin with a scale factor of 2.

Explanation:

Step1: Identify original vertices

First, find the coordinates of the original triangle's vertices. Let's assume the original vertices (from the grid) are, for example, \( (6, 8) \), \( (8, 8) \), and \( (7, 6) \) (we'll confirm by looking at the grid: the base seems between x=6 - 8, y=8, and the tip at x=7, y=6).

Step2: Apply dilation rule

Dilation centered at the origin with scale factor \( k = 2 \) means each coordinate \( (x, y) \) becomes \( (k \cdot x, k \cdot y) \). So:

• For \( (6, 8) \): \( (2 \cdot 6, 2 \cdot 8) = (12, 16) \)
• For \( (8, 8) \): \( (2 \cdot 8, 2 \cdot 8) = (16, 16) \)
• For \( (7, 6) \): \( (2 \cdot 7, 2 \cdot 6) = (14, 12) \)

Step3: Plot new vertices

Plot the points \( (12, 16) \), \( (16, 16) \), and \( (14, 12) \) on the grid and connect them to form the dilated triangle.

Answer:

To draw the dilated triangle:

1. Find original vertices (e.g., \( (6,8) \), \( (8,8) \), \( (7,6) \)).
2. Multiply each coordinate by 2: \( (12,16) \), \( (16,16) \), \( (14,12) \).
3. Plot these new points and connect them.

(Note: The actual drawing involves marking these points on the grid provided. The key is applying the dilation rule \( (x,y) \to (2x, 2y) \) to each vertex of the original triangle.)