Question

Point rr is located at (4,2) on the coordinate plane. Point rr is reflected over the xx-axis to create point r', then point r' is reflected over the yy-axis to create point r''. What ordered pair describes the location of r''?

Option 1: (-4, 2)
Option 2: (4, -2)
Option 3: (-4, -2)
Option 4: (4, 2)

Answer 1

After reflecting the initial point (4,2) first over the x-axis and then over the y-axis, the final coordinates of the point r'' are (-4, -2).

Step-by-step explanation:

The student's question involves a sequence of reflections of a point across the coordinate axes. The point rr is initially located at (4,2). When this point is reflected over the x-axis, the y-coordinate changes sign, resulting in point r' located at (4, -2). Then, reflecting point r' over the y-axis changes the x-coordinate's sign, giving us point r'' at (-4, -2).

Therefore, the ordered pair describing the location of r'' after these reflections is Option 3: (-4, -2).