Question

A rectangle is graphed on a coordinate plane. The table shows the original vertices and the new vertices after a scale factor with center of dilation at (0, 0) is applied.

Answer 1

To help you understand the transformation of the rectangle through dilation, let's break down the process of how a rectangle's vertices change under dilation from the center (0, 0) with a certain scale factor.

Given the original vertices of the rectangle, let's denote them as:

- \( A(x_1, y_1) \)
- \( B(x_2, y_2) \)
- \( C(x_3, y_3) \)
- \( D(x_4, y_4) \)

When you apply a dilation with a scale factor \( k \) from the center (0, 0), the new coordinates of each vertex can be calculated using the formula:

\[
A' = (k \cdot x_1, k \cdot y_1)
\]
\[
B' = (k \cdot x_2, k \cdot y_2)
\]
\[
C' = (k \cdot x_3, k \cdot y_3)
\]
\[
D' = (k \cdot x_4, k \cdot y_4)
\]

Where \( A', B', C', D' \) are the new vertices after dilation.

If you have specific vertex coordinates and a scale factor, you could apply this formula to find the new positions of the rectangle's vertices. If there's a specific example or data table you would like to examine, please provide the details, and I can assist you with the calculations!