A line segment is dilated by a scale factor of 2 centered at a point NOT on the line segment. Which statement regarding the relationship between the given line segment and its image is true?
1) The line segments are perpendicular, and the image is one-half the length of the given line segment.
2)The line segments are perpendicular, and the image is twice the length of the given line segment.
3)The line segments are parallel, and the image is twice the length of the given line segment.
4)The line segments are parallel, and the image is one-half the length of the given line segment.

The relationship between the given line segment and its image is (3)The line segments are parallel, and the image is twice the length of the given line segment.

The scale of dilation is given as: [tex]\mathbf{k = 2}[/tex]

This means that:

The image of the line will be twice the length of the pre-image

Also, we have that:

The center of dilation is not on the pre-image

This means that:

The image of the line will be parallel to the pre-image

Hence, the true statement is: (3)