The question asks to determine the rule that describes the reflection of triangle $MKJ$ across the x-axis to form triangle $M'K'J'$.

Coordinates of triangle $MKJ$:

• $M(-6, -2)$
• $K(-4, -2)$
• $J(-5, -4)$

When reflecting a point across the x-axis, the rule applied is:

• The x-coordinate remains the same.
• The y-coordinate changes its sign (from positive to negative or vice versa).

Thus, the reflection rule is: $(x, y) \rightarrow (x, -y)$

Applying the rule:

• $M(-6, -2) \rightarrow M'(-6, 2)$
• $K(-4, -2) \rightarrow K'(-4, 2)$
• $J(-5, -4) \rightarrow J'(-5, 4)$

Answer:

The transformation rule that describes this reflection is $(x, y) \rightarrow (x, -y)$, which corresponds to Option D.

Would you like more details on reflection transformations? Here are some related questions for further practice:

1. What is the rule for reflecting a point over the y-axis?
2. How would the coordinates change if you reflect across the origin?
3. What is the effect of reflecting over the line $y = x$?
4. Can you reflect a triangle across a vertical line other than the y-axis? How would that change the rule?
5. How do the coordinates of a point change when reflected across both axes?

Tip: When reflecting a shape, only the coordinate opposite to the axis of reflection changes sign.