Question

On a coordinate plane, the image rectangle has points (negative 3, 5), (negative 3, negative 5), (3, 5), (3, negative 5). Scale factor = 5.
For the given image and scale factor, which ordered pair is one of the pre-image vertices if the center of the pre-image is also the origin?
(Three-fifths, 1)
(Five-thirds, 1)
(1, 1)
(5, 1)

Answer 1

To find the pre-image vertices of the given image rectangle after scaling, we need to know that the center of the pre-image is the origin (0, 0) and that the scale factor is 5.

The points of the image rectangle are:
- (-3, 5)
- (-3, -5)
- (3, 5)
- (3, -5)

To find the pre-image points, we can use the formula for scaling:
\[
\text{pre-image} = \frac{\text{image}}{\text{scale factor}}
\]

Since the scale factor is 5, we divide each coordinate of the image points by 5.

Let's compute the pre-image points:

1. For point (-3, 5):
\[
\left(-\frac{3}{5}, \frac{5}{5}\right) = \left(-\frac{3}{5}, 1\right)
\]

2. For point (-3, -5):
\[
\left(-\frac{3}{5}, -\frac{5}{5}\right) = \left(-\frac{3}{5}, -1\right)
\]

3. For point (3, 5):
\[
\left(\frac{3}{5}, \frac{5}{5}\right) = \left(\frac{3}{5}, 1\right)
\]

4. For point (3, -5):
\[
\left(\frac{3}{5}, -\frac{5}{5}\right) = \left(\frac{3}{5}, -1\right)
\]

The pre-image vertices we found are:
- \((-3/5, 1)\)
- \((-3/5, -1)\)
- \((3/5, 1)\)
- \((3/5, -1)\)

Now, we can check the given options for matching points:

- \((3/5, 1)\)
- \((5/3, 1)\)
- \((1, 1)\)
- \((5, 1)\)

Among the options, \((3/5, 1)\) matches one of the calculated pre-image vertices.

Thus, **the ordered pair that is one of the pre-image vertices is \((3/5, 1)\)**.