https://file.aiquickdraw.com/mathbot/file/1729166042259z5cu6exy.jpg

Suppose the parallelogram on the coordinate plane was dilated with respect to the origin using a magnitude of 12 . What would be the coordinates of vertex D′ ?

To find the coordinates of vertex \( D' \) after a dilation with respect to the origin by a scale factor of \( k = 12 \), we can use the dilation formula:

\[
(x', y') = (k \cdot x, k \cdot y)
\]

For vertex \( D \), with coordinates \( (2, -2) \):

1. **Apply the dilation** by multiplying each coordinate of \( D \) by the scale factor \( 12 \):
   \[
   x' = 12 \cdot 2 = 24
   \]
   \[
   y' = 12 \cdot (-2) = -24
   \]

2. So, the coordinates of \( D' \) are:
   \[
   D' = (24, -24)
   \]

Would you like further details on dilation or other points in the shape?

---

**Further Questions:**
1. How would the coordinates of point \( A \) change under the same dilation?
2. What are the new coordinates of point \( B \) after applying a dilation of 12?
3. What happens to the area of the parallelogram after a dilation with this factor?
4. What would be the coordinates of \( C' \) after a dilation of 12?
5. How does a dilation centered at a different point affect the coordinates of each vertex?

**Tip:** When dilating points with respect to the origin, simply multiply each coordinate by the scale factor!

Suppose the parallelogram on the coordinate plane was dilated with respect to the origin using a magnitude of 12. What would be the coordinates of vertex D'?

Learn how to find the new coordinates of vertex D' of a parallelogram after a dilation with a scale factor of 12. Understand the process of using the dilation formula to determine the transformed points with respect to the origin. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation