Answer :

The length of segment A'E' of the new formed pentagon is 5 units.

How to find the length of the line segment?

We are given that:

Pentagon A’B′C′D′E’, is the image of pentagon ABCDE under a dilation with a scale factor of 5/2.

From the attached graph, we see that the coordinates of the points A and E, in the pentagon ABCDE with reference to point A are;

A- (0, 0)

E- (0, 2)

The length of the segment AE is:

AE = √((2-0)² + (0 - 0)²)

AE = √2²

AE = 2

When a pentagon ABCDE is dilated to pentagon A'B'C'D'E' with a scale factor of 5/2, we have;

Length of segment A'E' = 5/2 × Length of segment AE

Thus;

Length of segment A'E' = 5/2 × 2

Length of segment A'E' = 5 units.

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Complete question is:

Pentagon A’B′C′D′E’, is the image of pentagon ABCDE under a dilation with a scale factor of 5/2.

Find the length of the line segment A'E'.