Question

A dilation with a scale factor of 4 is applied to the 3 line segment show on the resulting image are P'Q', A'B', And M'N'. Drag and drop the measures to correctly match the lengths of The images

Answer 1

Given:

Scale factor = 4 (Dilation)

PQ = 2 cm

AB = 1.5 cm

MN = 3 cm

Find-:

`P^(\prime)Q^(\prime),A^(\prime)B^(\prime)\text{ and }M^(\prime)N^(\prime)`

Explanation-:

Scale factor = 4

So,

`\begin{gathered} P^(\prime)Q^(\prime)=4PQ \\ \\ A^(\prime)B^(\prime)=4AB \\ \\ M^(\prime)N^(\prime)=4MN \end{gathered}`

So the value is:

`\begin{gathered} P^(\prime)Q^(\prime)=4PQ \\ \\ P^(\prime)Q^(\prime)=4*2 \\ \\ P^(\prime)Q^(\prime)=8\text{ cm} \end{gathered}`
`\begin{gathered} A^(\prime)B^(\prime)=4AB \\ \\ A^(\prime)B^(\prime)=4*1.5 \\ \\ A^(\prime)B^(\prime)=6\text{ cm} \end{gathered}`
`\begin{gathered} M^(\prime)N^(\prime)=4MN \\ \\ M^(\prime)N^(\prime)=4*3 \\ \\ M^(\prime)N^(\prime)=12\text{ cm} \end{gathered}`