Question

write the coordinates of the vertices after a dilation with a scale factor of \\(\frac{1}{3}\\), centered at the origin. \\(l(\square, \square)\\) \\(m(\square, \square)\\) \\(n(\square, \square)\\)

Explanation:

Step1: Find original coordinates

From the graph, we identify the original coordinates:

• \( L(-9, -9) \) (since it's at x=-9, y=-9)
• \( M(-9, 9) \) (x=-9, y=9)
• \( N(9, -9) \) (x=9, y=-9)

Step2: Apply dilation formula

The dilation formula centered at the origin with scale factor \( k \) is \( (x', y') = (k \cdot x, k \cdot y) \), where \( k = \frac{1}{3} \).

For \( L(-9, -9) \):

\( x' = \frac{1}{3} \times (-9) = -3 \)
\( y' = \frac{1}{3} \times (-9) = -3 \)
So, \( L'(-3, -3) \)

For \( M(-9, 9) \):

\( x' = \frac{1}{3} \times (-9) = -3 \)
\( y' = \frac{1}{3} \times 9 = 3 \)
So, \( M'(-3, 3) \)

For \( N(9, -9) \):

\( x' = \frac{1}{3} \times 9 = 3 \)
\( y' = \frac{1}{3} \times (-9) = -3 \)
So, \( N'(3, -3) \)

Answer:

\( L'(-3, -3) \)
\( M'(-3, 3) \)
\( N'(3, -3) \)