Question

The coordinates for the endpoints of LM are L (-2, -3) and M (4, 5). LM is dilated by a scale factor of ( 1/ 2) from center of dilation (3, -2) to form Segment L′ M′ . Which statement is not true?

The length of Segment L′ M′ is one-half the length of Segment LM .
The length of Segment L′ M′ is twice the length of Segment LM .
The slope of Segment L′ M′ is the same as the slope of Segment LM .
Segment L′ M′ is parallel to Segment LM .

Answer 1

Dilation is a transformation that preserves angles. This means that:

• ∠OLM≅∠OL'M';
• ∠OML≅∠OM'L',

where O(3,-2) is a center of dilation.

These pairs of congruent angles are alternate angles formed with lines LM and L'M' and two transversals OL and OL'. Thus, lines LM and L'M' must be parallel. So option D is true.

If lines LM and L'M' are parallel, then their slopes are equal and option C is true.

Now, since a scale factor is 1/2, the image segment L'M' has length that is one-half of the length of segment LM. Therefore, option A is true and option B is false.

Answer: statement B is false.