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

Answer: This is the choice that is not true: "The length of Segment L′ M′ is twice the length of Segment LM".

Justification:

Dilataions are transformations that preserve the directions of the segments. Hence, the image of a transformation has the same shape as the pre-image but different size.

When the scale factor is less than 1 (in this case is 1/2 = 0.5) the image is shrinked as per such factor.

To find the lenghts of the image of the dilation by a scale factor of 1/2 multiply the coordinates by 1/2: (x,y) → (x/2, y/2).

That means that the length of segment  L′ M′ is one-half the length of the segment LM; hence the first option is true and the second option is false.

The resulting segments are parallel which means that their slopes are the same, so the third and fourth statements ("The slope of Segment L′ M′ is the same as the slope of Segment LM" and "Segment L′ M′ is parallel to Segment LM") are true too.