Question

Rectangle LMNO is rotated 90° clockwise around the origin to create rectangle L'M'N'O'. Which statement would best describe the relationship between points N and N'?
They are equidistant from origin.
They are midpoints of segment ON and segment O prime N prime.
They are equidistant from point O.
They are midpoints of segment LN and segment L prime N prime.

Answer 1

Answer:

   Segment LL' and segment OO' are congruent (same length) and parallel (same inclination).

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Explanation:

The transformation described by the rule  (x, y) → (x + 2, y + 2) is a translation two units to the right and two units up.

That means that, to create rectangle L'M'N'O', every point of the reactangle LMNO is translated the same amount in the same direction; thus, this is a rigid transformation where angles, lengths, size, shape, and orientation are kept.

Then a segment drawn from point L to L' will have the same length and the same orientation (inclination) of a segment drawn from the point O to O'. Thus, these two segments are parallel and congruent.