https://file.aiquickdraw.com/mathbot/file/1726070385517fklk6mja.jpg

Let's analyze the transformation process described in the image to find the coordinates of vertex \( J' \):

### Initial steps:
- **Triangle \( JKL \)** is:
  - **Rotated 90° clockwise** about the origin,
  - **Translated 5 units to the right**,
  - **Reflected over the x-axis**.

We will break down each transformation applied to vertex \( J \), following the given order.

### Step 1: 90° clockwise rotation about the origin
When a point \( (x, y) \) is rotated 90° clockwise around the origin, the coordinates transform as follows:
\[
(x, y) \rightarrow (y, -x)
\]
- The original coordinates of \( J \) are \( (-3, -1) \) (from observation of the graph).
- After 90° clockwise rotation:
\[
(-3, -1) \rightarrow (-1, 3)
\]

### Step 2: Translation 5 units to the right
To translate the point 5 units to the right, add 5 to the x-coordinate:
\[
(-1, 3) \rightarrow (-1 + 5, 3) = (4, 3)
\]

### Step 3: Reflection over the x-axis
When reflecting a point \( (x, y) \) over the x-axis, the y-coordinate changes its sign:
\[
(x, y) \rightarrow (x, -y)
\]
- After reflecting \( (4, 3) \) over the x-axis:
\[
(4, 3) \rightarrow (4, -3)
\]

Thus, the final coordinates of vertex \( J' \) are \( (4, -3) \).

### Conclusion:
The answer isn't directly listed among the options provided in the multiple-choice answers. This may indicate a typo or a misalignment in the image text.

Would you like to clarify any details or ask further questions? Here are some additional questions for practice:

1. What are the steps for performing a 180° rotation about the origin?
2. How does reflecting over the y-axis affect the coordinates of a point?
3. If a point is reflected over both the x-axis and y-axis, what transformation does it undergo?
4. What is the effect of translating a point left and down by some units?
5. How would the final image change if the reflection happened before the rotation?

**Tip:** Always double-check graph transformations by visualizing or plotting each step if possible.

Triangle JKL is rotated 90° clockwise about the origin, translated 5 units to the right, and reflected over the x-axis. The image that results is ΔJ'K'L'. What are the coordinates of vertex J' on the image?

Learn how to transform a triangle with 90° clockwise rotation, translation, and reflection over the x-axis. This problem involves key geometric transformations and is suitable for students in Grades 7-9.

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