Question

Segment AB measures 3 cm. Point O is the center of dilation. How long is the image of AB after a dilation with . . .

Use decimal notation if necessary.



a. scale factor 5?

Answer 1

The image of AB will be 15 cm long after dilation by a scale factor of 5.

Explanation:

We know that when an object is dilated by a scale factor, it gets reduced, stretched, or remains the same, depending upon the value of the scale factor.

• If the scale factor > 1, the image is enlarged

• If the scale factor is between 0 and 1, it gets shrunk

• If the scale factor = 1, the object and the image are congruent

Rule to calculate the mage of the segment AB after dilation of the segment AB by a scale factor 5 centered at the origin

AB = length → A'B' = 5(length)

It means the length of the image of the segment AB can be determined by multiplying the length of the original segment AB by 5.

so

AB = 3 cm

Thus, the length of image A'B' will be:

A'B' = 5(3) = 15 cm

Therefore, the image of AB will be 15 cm long after dilation by a scale factor of 5.