Question

A point, P(7,-4) is reflected across the x-axis, then across the line y=x. Which transformation is equivalent to this series of reflections?

Answer 1

The transformation equivalent to reflecting point P(7,-4) across the x-axis and then across the line y=x is a reflection across the line y=x resulting in the new coordinates (4,7).

Step-by-step explanation:

To determine the transformation that is equivalent to reflecting point P(7,-4) across the x-axis, and then across the line y=x, we need to understand how each reflection affects the coordinates of the point.

When reflecting across the x-axis, the x-coordinate remains the same, but the y-coordinate changes sign. So, the new coordinates are (7,4).

Next, when reflecting across the line y=x, the x-coordinate is replaced by the y-coordinate, and the y-coordinate is replaced by the x-coordinate. So, the new coordinates are (4,7).

Therefore, the transformation that is equivalent to this series of reflections is a reflection across the line y=x, resulting in the new coordinates (4,7).