Question

write the coordinates of the vertices after a dilation with a scale factor of 4, centered at the origin.

Explanation:

Step1: Identify original coordinates

First, find the original coordinates of points \( L \), \( M \), and \( N \) from the graph.

• Point \( L \): \( (-2, -1) \)
• Point \( M \): \( (-2, 2) \)
• Point \( N \): \( (0, -2) \)

Step2: Apply dilation formula

The rule for dilation centered at the origin with scale factor \( k \) is \( (x, y) \to (k \cdot x, k \cdot y) \). Here, \( k = 4 \).

For point \( L(-2, -1) \):

Multiply each coordinate by 4:
\( x \)-coordinate: \( 4 \times (-2) = -8 \)
\( y \)-coordinate: \( 4 \times (-1) = -4 \)
So, \( L' = (-8, -4) \)

For point \( M(-2, 2) \):

Multiply each coordinate by 4:
\( x \)-coordinate: \( 4 \times (-2) = -8 \)
\( y \)-coordinate: \( 4 \times 2 = 8 \)
So, \( M' = (-8, 8) \)

For point \( N(0, -2) \):

Multiply each coordinate by 4:
\( x \)-coordinate: \( 4 \times 0 = 0 \)
\( y \)-coordinate: \( 4 \times (-2) = -8 \)
So, \( N' = (0, -8) \)

Answer:

The coordinates of the vertices after dilation are \( L'(-8, -4) \), \( M'(-8, 8) \), and \( N'(0, -8) \).