Question

consider rectangle pqrs. a reflection across which line carries rectangle pqrs onto itself? x = 2 y = 3 y = 2 x = 3

Explanation:

Step1: Recall property of rectangle

A rectangle has two lines of symmetry, one vertical and one horizontal through its center.

Step2: Analyze vertical line of symmetry

If the center - x - coordinate of the rectangle is \(x = 3\), a reflection across \(x = 3\) will carry the rectangle onto itself. The vertical line \(x = 3\) divides the rectangle into two congruent halves such that each point on one side of the line has a corresponding point on the other side at the same distance from the line.

Step3: Analyze horizontal line of symmetry

There is no horizontal line among the options that is a line of symmetry for the rectangle in the context of the problem.

Answer:

x = 3