Question

1. sketch the image of line segment bc after a dilation about point a by a scale factor of 3.

Explanation:

Step1: Identify coordinates

First, find the coordinates of points \( A \), \( B \), and \( C \) from the grid.

• \( A(1, 1) \)
• \( B(2, 2) \)
• \( C(5, 2) \)

Step2: Calculate vector from \( A \) to \( B \)

The vector \( \overrightarrow{AB} \) is \( (2 - 1, 2 - 1) = (1, 1) \). After dilation with scale factor 3, the new vector \( \overrightarrow{AB'} \) is \( 3 \times (1, 1) = (3, 3) \). So, the coordinates of \( B' \) (image of \( B \)) are \( A + \overrightarrow{AB'} = (1 + 3, 1 + 3) = (4, 4) \).

Step3: Calculate vector from \( A \) to \( C \)

The vector \( \overrightarrow{AC} \) is \( (5 - 1, 2 - 1) = (4, 1) \). After dilation with scale factor 3, the new vector \( \overrightarrow{AC'} \) is \( 3 \times (4, 1) = (12, 3) \). So, the coordinates of \( C' \) (image of \( C \)) are \( A + \overrightarrow{AC'} = (1 + 12, 1 + 3) = (13, 4) \).

Step4: Sketch the segment

Draw the line segment connecting \( B'(4, 4) \) and \( C'(13, 4) \).

Answer:

The image of segment \( BC \) after dilation about \( A \) with scale factor 3 is the segment connecting \( (4, 4) \) and \( (13, 4) \). (To sketch, plot these two points and draw the line segment between them.)