Question

the figure below is dilated by a factor of 2 centered at the origin. plot the resulting image.
click twice to plot a segment.
click a segment to delete it.

Explanation:

Step1: Identify coordinates

First, find the coordinates of the vertices. From the graph:

• Point \( F \): \((-1, 2)\)
• Point \( E \): \((2, 0)\)
• Point \( G \) (the bottom vertex): \((0, -3)\) (assuming the third vertex is at \((0, -3)\) from the graph)

Step2: Apply dilation factor

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

• For \( F(-1, 2) \): New coordinates \( F' = (2 \cdot (-1), 2 \cdot 2) = (-2, 4) \)
• For \( E(2, 0) \): New coordinates \( E' = (2 \cdot 2, 2 \cdot 0) = (4, 0) \)
• For \( G(0, -3) \): New coordinates \( G' = (2 \cdot 0, 2 \cdot (-3)) = (0, -6) \)

Step3: Plot the new points

Plot \( F'(-2, 4) \), \( E'(4, 0) \), and \( G'(0, -6) \) on the coordinate plane and connect them to form the dilated triangle.

Answer:

To plot the dilated image:

1. Find the original vertices: \( F(-1, 2) \), \( E(2, 0) \), \( G(0, -3) \).
2. Dilate each by \( 2 \):

• \( F'(-2, 4) \)
• \( E'(4, 0) \)
• \( G'(0, -6) \)

1. Plot these new points and connect them to form the triangle.

(Note: Since this is a plotting task, the final answer involves plotting the points \( (-2, 4) \), \( (4, 0) \), and \( (0, -6) \) and connecting them.)