Question

After a reflection across the x-axis, what are the coordinates of the vertices?

a) E'(-9, -8), F'(-9, -1), G'(-1, -1), H'(-1, 8)
b) E'(-9, -8), F'(-9, -1), G'(-1, -1), H'(-1, -8)
c) E'(-9, 8), F'(-9, 1), G'(-1, 1), H'(-1, -8)
d) E'(-9, 8), F'(-9, 1), G'(-1, 1), H'(-1, -1)

Answer 1

After reflecting the vertices across the x-axis, the y-coordinates change signs while the x-coordinates remain the same, resulting in the vertices E'(-9, -8), F'(-9, -1), G'(-1, -1), H'(-1, -8).

Step-by-step explanation:

When an object is reflected across the x-axis in a coordinate system, each point of the object has its y-coordinate changed to the opposite sign while the x-coordinate remains the same. We apply this to the vertices given in the question.

• For E'(-9, 8), after reflection, it becomes E'(-9, -8).
• For F'(-9, 1), after reflection, it becomes F'(-9, -1).
• For G'(-1, 1), after reflection, it becomes G'(-1, -1).
• For H'(-1, -8), after reflection, it remains H'(-1, -8) because it was already below the x-axis.

Therefore, the correct coordinates of the vertices after the reflection across the x-axis are E'(-9, -8), F'(-9, -1), G'(-1, -1), and H'(-1, -8). The correct answer is therefore option (b).