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:

To solve the dilation of the figure by a factor of 2 centered at the origin, we follow these steps:

Step 1: Identify the coordinates of the vertices

First, we determine the coordinates of points \( B \), \( D \), and \( C \) from the graph:

• Point \( B \): \( (-2, -2) \)
• Point \( D \): \( (-2, 3) \)
• Point \( C \): \( (3, -1) \)

Step 2: Apply the dilation rule

The rule for dilation centered at the origin with a scale factor \( k \) is \( (x, y)
ightarrow (k \cdot x, k \cdot y) \). Here, \( k = 2 \).

• For point \( B(-2, -2) \):

$$ (2 \cdot (-2), 2 \cdot (-2)) = (-4, -4) $$

• For point \( D(-2, 3) \):

$$ (2 \cdot (-2), 2 \cdot 3) = (-4, 6) $$

• For point \( C(3, -1) \):

$$ (2 \cdot 3, 2 \cdot (-1)) = (6, -2) $$

Step 3: Plot the new points

Plot the points \( (-4, -4) \), \( (-4, 6) \), and \( (6, -2) \) on the coordinate plane and connect them to form the dilated figure.

Final Answer

The dilated figure has vertices at \( (-4, -4) \), \( (-4, 6) \), and \( (6, -2) \). Plot these points and connect them to see the dilated image.

Answer:

To solve the dilation of the figure by a factor of 2 centered at the origin, we follow these steps:

Step 1: Identify the coordinates of the vertices

First, we determine the coordinates of points \( B \), \( D \), and \( C \) from the graph:

• Point \( B \): \( (-2, -2) \)
• Point \( D \): \( (-2, 3) \)
• Point \( C \): \( (3, -1) \)

Step 2: Apply the dilation rule

The rule for dilation centered at the origin with a scale factor \( k \) is \( (x, y)
ightarrow (k \cdot x, k \cdot y) \). Here, \( k = 2 \).

• For point \( B(-2, -2) \):

$$ (2 \cdot (-2), 2 \cdot (-2)) = (-4, -4) $$

• For point \( D(-2, 3) \):

$$ (2 \cdot (-2), 2 \cdot 3) = (-4, 6) $$

• For point \( C(3, -1) \):

$$ (2 \cdot 3, 2 \cdot (-1)) = (6, -2) $$

Step 3: Plot the new points

Plot the points \( (-4, -4) \), \( (-4, 6) \), and \( (6, -2) \) on the coordinate plane and connect them to form the dilated figure.

Final Answer

The dilated figure has vertices at \( (-4, -4) \), \( (-4, 6) \), and \( (6, -2) \). Plot these points and connect them to see the dilated image.