Question

On a coordinate plane, the pre-image square has points (0, 0), (0, 3), (3, 3), (3, 0). Scale factor = 2.
Consider the given pre-image dilated by a scale factor of 2, and answer the questions.


After applying the scale factor, what is the image?

enlargement
What will be the new coordinate of the vertex at (3, 3) if the vertex at (0, 0) remains the same?

Answer 1

To find the coordinates of the image after dilation with a scale factor of 2 from the origin (0, 0), we can simply multiply the coordinates of each vertex of the pre-image by the scale factor.

The pre-image square has the following vertices:
- (0, 0)
- (0, 3)
- (3, 3)
- (3, 0)

Applying the scale factor of 2 to each vertex:

1. For (0, 0):
\[
(0 \cdot 2, 0 \cdot 2) = (0, 0)
\]

2. For (0, 3):
\[
(0 \cdot 2, 3 \cdot 2) = (0, 6)
\]

3. For (3, 3):
\[
(3 \cdot 2, 3 \cdot 2) = (6, 6)
\]

4. For (3, 0):
\[
(3 \cdot 2, 0 \cdot 2) = (6, 0)
\]

So, the coordinates of the new image after dilation are:
- (0, 0)
- (0, 6)
- (6, 6)
- (6, 0)

### Summary:
- The image after applying the scale factor of 2 is the square with vertices:
- (0, 0)
- (0, 6)
- (6, 6)
- (6, 0)

### New Coordinate of the Vertex:
- The new coordinate of the vertex originally at (3, 3) is (6, 6) when considering that the vertex at (0, 0) remains the same.