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 graph) are, for example, \( (6, 8) \), \( (8, 8) \), and \( (7, 5) \) (we'll confirm via grid: each square is 1 unit).

Step2: Apply dilation rule

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

• For \( (6, 8) \): New coordinate is \( (2 \cdot 6, 2 \cdot 8) = (12, 16) \)
• For \( (8, 8) \): New coordinate is \( (2 \cdot 8, 2 \cdot 8) = (16, 16) \)
• For \( (7, 5) \): New coordinate is \( (2 \cdot 7, 2 \cdot 5) = (14, 10) \)

Step3: Plot new vertices

Plot the points \( (12, 16) \), \( (16, 16) \), and \( (14, 10) \) on the grid and connect them to form the dilated triangle.

Answer:

The dilated triangle has vertices at \( (12, 16) \), \( (16, 16) \), and \( (14, 10) \) (plotted and connected on the grid as per the dilation rule).