Question

write the coordinates of the vertices after a dilation with a scale factor of 3, centered at the origin.

Explanation:

Step1: Identify original coordinates

From the graph, we can see the original coordinates:

• \( J(-3, 1) \)
• \( K(-3, 2) \)
• \( L(-2, 2) \)

Step2: Apply dilation formula

The formula for dilation centered at the origin with scale factor \( k \) is \( (x, y) \to (k \cdot x, k \cdot y) \). Here, \( k = 3 \).

For \( J(-3, 1) \):
\( x' = 3 \times (-3) = -9 \)
\( y' = 3 \times 1 = 3 \)
So, \( J'(-9, 3) \)

For \( K(-3, 2) \):
\( x' = 3 \times (-3) = -9 \)
\( y' = 3 \times 2 = 6 \)
So, \( K'(-9, 6) \)

For \( L(-2, 2) \):
\( x' = 3 \times (-2) = -6 \)
\( y' = 3 \times 2 = 6 \)
So, \( L'(-6, 6) \)

Answer:

The coordinates after dilation are \( J'(-9, 3) \), \( K'(-9, 6) \), and \( L'(-6, 6) \).