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.