Question

Select the coordinates A′ and B′ after dilation of the line segment AB with a scale factor of 13 , centered at the origin where the endpoints are A(−6,3) and B(−12,9

Answer 1

To find the coordinates \( A' \) and \( B' \) after a dilation of the line segment \( AB \) with a scale factor of \( 13 \) centered at the origin, we can apply the dilation formula:

\[
A' = (x_A \cdot k, y_A \cdot k) \quad \text{and} \quad B' = (x_B \cdot k, y_B \cdot k)
\]

where \( (x_A, y_A) \) and \( (x_B, y_B) \) are the original coordinates of points \( A \) and \( B \), and \( k \) is the scale factor.

For point \( A(-6, 3) \):
- \( x_A = -6 \)
- \( y_A = 3 \)

For point \( B(-12, 9) \):
- \( x_B = -12 \)
- \( y_B = 9 \)

Given \( k = 13 \):

Now, let's calculate the new coordinates:

1. For point \( A' \):
\[
A' = (-6 \cdot 13, 3 \cdot 13) = (-78, 39)
\]

2. For point \( B' \):
\[
B' = (-12 \cdot 13, 9 \cdot 13) = (-156, 117)
\]

Thus, the coordinates after dilation are:
- \( A'(-78, 39) \)
- \( B'(-156, 117) \)