Question

100 PTS!!A dilation with a scale factor of 4 is applied to the three line segments shown. The resulting images are P’Q’ and A’B’ and M’N’.

Drag and drop the measure to correctly match the lights of the images.

P’Q’ ->
A’B’->
M’N->

Choices: 0.375cm, 0.5cm, 0.75cm, 6cm, 8cm, 12cm.

Answer 1

As no points are shown so only steps can be provided to solve

So if A(x,y) is dilated by scale factor 4 then 4 is multiplied with A(x,y)

So new coordinates are (4x,4y)

So

if length of segment was x then after dilation new length is 4x

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