All side lengths in quadrilateral PQRS measure 4 units. A transformation maps PQRS to P'Q'R'S'. All sides of P'Q'R'S' measure 1 unit.

Is the transformation an isometric transformation? Explain.

Yes, the side lengths in the two figures are proportional.
Yes, one figure maps to the other.
No, the side lengths are not preserved.
No, the angles are not preserved.

1 answer

To determine whether the transformation that maps quadrilateral PQRS to quadrilateral P'Q'R'S' is an isometric transformation, we need to recall what an isometric transformation is. An isometric transformation is one that preserves lengths, meaning that the distances between points in the original figure remain the same in the transformed figure.

In this case, we have:

  • The side lengths of quadrilateral PQRS measure 4 units each.
  • The side lengths of quadrilateral P'Q'R'S' measure 1 unit each.

The lengths of the sides are not preserved during the transformation, as the side lengths changed from 4 units to 1 unit (a difference of a factor of 4). This indicates that the transformation does not maintain the distances between the points in the two figures.

Therefore, the correct conclusion is:

No, the side lengths are not preserved.