The problem asks to find the coordinates of the vertices of triangle ABC after reflecting it over the x-axis.

The original triangle ABC has the following coordinates:

• $A(2, 0)$
• $B(-1, 5)$
• $C(4, 3)$

Reflection Over the X-axis:

When reflecting a point over the x-axis, the x-coordinate remains unchanged, but the y-coordinate becomes its opposite (negation). Therefore, the new coordinates for each point after reflection are:

• $A'(2, -0) = A'(2, 0)$ (since the y-coordinate of 0 stays 0)
• $B'(-1, -5)$
• $C'(4, -3)$

Conclusion:

The new coordinates after reflection are:

• $A'(2, 0)$
• $B'(-1, -5)$
• $C'(4, -3)$

The correct option is B).

Would you like more details or have any other questions?

Here are five related questions:

1. How do you reflect a point over the y-axis?
2. What happens to the coordinates when reflecting over the origin?
3. Can you explain how to reflect over the line $y = x$?
4. How would the coordinates change if reflected over the line $y = -x$?
5. What is the difference between translation and reflection in geometry?

Tip: When reflecting across the x-axis, only the y-coordinate changes its sign, while the x-coordinate remains unchanged.