Question

A line segment is dilated by a factor of 4 and the center of the dilation is a point on the line segment. Which of the following is the result of this dilation?
a. A line segment that is 4 times longer and in the some position as the original line segment
b. a line segment that is 4 times longer and perpendicular to the original line segment, crossing the original line segment at the center of the dilation point
c. a congruent line segment that is parallel to the original line segment
d. a line segment that is 4 times longer and parallel to the original line segment

Answer 1

Answer:

a.  A line segment that is 4 times longer and in the same position as the original line segment.

Step-by-step explanation:

In dilation, when the center of dilation lies on the line segment,  the dilated line segment remains at the same position.

Also, the dilated line segment has length 4 times that of original line segment if the factor of dilation is 4.

As shown is the figure attached:

PQ is the line segment. Center of dilation is 0.

0P' is four times that of OP and OQ' is four times that of OQ.

The dilated line segment is at the same position.