Question

write the coordinates of the vertices after a dilation with a scale factor of \\(\frac{1}{2}\\), centered at the origin.

Explanation:

Step1: Find original coordinates

From the graph, \( A(-4, -6) \), \( B(0, -6) \), \( C(0, -10) \).

Step2: Apply dilation formula

Dilation centered at origin: \( (x,y) \to (\frac{1}{2}x, \frac{1}{2}y) \).

• For \( A \): \( x' = \frac{1}{2}(-4) = -2 \), \( y' = \frac{1}{2}(-6) = -3 \), so \( A'(-2, -3) \).
• For \( B \): \( x' = \frac{1}{2}(0) = 0 \), \( y' = \frac{1}{2}(-6) = -3 \), so \( B'(0, -3) \).
• For \( C \): \( x' = \frac{1}{2}(0) = 0 \), \( y' = \frac{1}{2}(-10) = -5 \), so \( C'(0, -5) \).

Answer:

\( A'(-2, -3) \)
\( B'(0, -3) \)
\( C'(0, -5) \)