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

Among the statements given, the one that is false is that the length of Segment L′M′ is twice the length of Segment LM. In reality, the length is halved due to the dilation factor of ½.

Step-by-step explanation:

When segment LM is dilated by a scale factor of ½ from the center of dilation at (3, -2) to form segment L′M′, the following statements can be evaluated:

• The length of Segment L′M′ is one-half the length of Segment LM. This statement is true due to the dilation factor of ½.
• The length of Segment L′M′ is twice the length of Segment LM. This statement is false because the scale factor reduces, rather than increases, the segment's length.
• The slope of Segment L′M′ is the same as the slope of Segment LM. This is true, as dilation maintains the slope of the segment.
• Segment L′M′ is parallel to Segment LM. This is also true, as maintaining the slope means the segments remain parallel post-dilation.

Therefore, the statement that the length of Segment L′M′ is twice the length of Segment LM is not true.

Answer 2

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.