Question

1. dilate abcd by scale factor of ½ and relabel the new points.
2. after the trans

must be true.

a. \\(\frac{ad}{ad}\\)

b. \\(\frac{pc}{pc}\\)

c. angl

d. angle
suppl

e. \\(\frac{ad}{ad}=\\)

f. \\(\frac{pd}{pd}=\\)

Explanation:

Step1: Recall Dilation Rules

Dilation about a point \( P \) (center of dilation) scales distances from \( P \) by the scale factor \( \frac{1}{2} \). For a point \( X \) on the figure, the image \( X' \) satisfies \( PX' = \frac{1}{2}PX \), and the line \( PX \) contains \( X' \).

Step2: Process Each Vertex

• Vertex \( A \): Draw line \( PA \). Measure \( PA \), then find \( A' \) such that \( PA' = \frac{1}{2}PA \) (closer to \( P \) than \( A \)).
• Vertex \( B \): Draw line \( PB \). Find \( B' \) with \( PB' = \frac{1}{2}PB \).
• Vertex \( C \): Draw line \( PC \). Find \( C' \) with \( PC' = \frac{1}{2}PC \).
• Vertex \( D \): Draw line \( PD \). Find \( D' \) with \( PD' = \frac{1}{2}PD \).

Step3: Relabel and Connect

Connect \( A' \), \( B' \), \( C' \), \( D' \) in order. The new figure \( A'B'C'D' \) is a dilation of \( ABCD \) with scale factor \( \frac{1}{2} \), similar to \( ABCD \) (same shape, smaller size, centered at \( P \)).

Answer:

To dilate \( ABCD \) by scale factor \( \frac{1}{2} \) about \( P \):

1. For each vertex \( A, B, C, D \), draw a line from \( P \) through the vertex.
2. Locate the new vertex (e.g., \( A' \) for \( A \)) such that the distance from \( P \) to the new vertex is half the distance from \( P \) to the original vertex.
3. Connect \( A', B', C', D' \) to form the dilated parallelogram \( A'B'C'D' \).

(Note: The exact coordinates/positions depend on the diagram’s scale, but the process follows the dilation rules.)