Question

A dilation with a scale factor of 4 is applied to the three line segments shown. The resulting images are P′Q′⎯⎯⎯⎯⎯⎯⎯⎯ , A′B′⎯⎯⎯⎯⎯⎯⎯ , and M′N′⎯⎯⎯⎯⎯⎯⎯⎯⎯ .

Answer 1

pq=8, ab=6, mn=12    you just multiply each line length by 4.

Answer 2

P'Q' ⇔ 8 cm

A'B' ⇔ 6 cm

M'N' ⇔ 12 cm

Explanation:

A dilation with a scale factor of 4 is applied to the three line segments PQ, AB and MN.

The length of PQ is given as: 2 cm.

The length of line segment AB is given as: 1.5 cm

The length of line segment MN is given as: 3 cm.

Now as there is a dilation with a scale factor of 4 to all the line segments this means that the resulting image will have length 4 times the length of these line segments.

PQ → P'Q'

⇒ Length of P'Q'= 8 cm. ( since 4×2=8)

AB → A'B'

⇒ Length of A'B'= 6 cm. ( since 1.5×4=6)

MN → M'N'

⇒ Length of M'N'= 12 cm. ( since 4×3=12)

Hence,

P'Q' ⇔ 8 cm

A'B' ⇔ 6 cm

M'N' ⇔ 12 cm