Question

write the coordinates of the vertices after a dilation with a scale factor of 2, centered at the origin.

Explanation:

Step1: Identify original coordinates

First, find the original coordinates of each vertex from the graph:

• \( J(-5, -5) \)
• \( K(3, -5) \)
• \( L(3, 5) \)
• \( M(-5, 5) \)

Step2: Apply dilation formula

The rule for dilation centered at the origin with scale factor \( k \) is \( (x, y) \to (kx, ky) \). Here, \( k = 2 \).

For \( J(-5, -5) \):
\( x' = 2 \times (-5) = -10 \), \( y' = 2 \times (-5) = -10 \), so \( J'(-10, -10) \)

For \( K(3, -5) \):
\( x' = 2 \times 3 = 6 \), \( y' = 2 \times (-5) = -10 \), so \( K'(6, -10) \)

For \( L(3, 5) \):
\( x' = 2 \times 3 = 6 \), \( y' = 2 \times 5 = 10 \), so \( L'(6, 10) \)

For \( M(-5, 5) \):
\( x' = 2 \times (-5) = -10 \), \( y' = 2 \times 5 = 10 \), so \( M'(-10, 10) \)

Answer:

The coordinates of the vertices after dilation are \( J'(-10, -10) \), \( K'(6, -10) \), \( L'(6, 10) \), and \( M'(-10, 10) \).