Question

Geometry question!

Quadrilateral QRST is dilated and translated to form similar figure Q'R'S'T'. What is the scale factor for the dilation? (see attachment)

**the answer is 1/3**

Answer 1

Since we know that dilation of a figure changes all sides of a figure by same factor.

Let us find out factor of dilation of our figure.

We will find side length QR of our quadrilateral QRST and its corresponding side QR' of quadrilateral Q'R'S'T'.

$\text{Length of QR}=5--1$

$\text{Length of QR}=5+1=6$

Let us find side length of Q'R'.

$\text{Length of Q'R'}=1--1$

$\text{Length of Q'R'}=1+1=2$

Let us compare both our side lengths to find factor of dilation,

$\frac{QR}{Q'R'}= \frac{6}{2}$

$\frac{QR}{Q'R'}= 3$

Upon cross multiplication we will get,

$QR=3\cdot Q'R'$

$Q'R'=\frac{1}{3} \cdot QR$

We can see that Q'R' is $\frac{1}{3}$ of Q'R'. Therefore, our factor of dilation is $\frac{1}{3}$.      

Answer 2

The scale factor is defined as the ratio of the length of a side of the first quadrilateral; figure to the length of the corresponding side of the quadrilateral.

The scale factor of a dilation is 3,

Given

Quadrilateral QRST is dilated and translated to form a similar figure Q'R'S'T'.

What is the scale factor?

The scale factor is defined as the ratio of the length of a side of the first quadrilateral; figure to the length of the corresponding side of the quadrilateral.

The length QR of our quadrilateral QRST and its corresponding side QR' of quadrilateral Q'R'S'T'.

Length of QR = 5 - (-1) = 5+1 = 6

And the length of the Q'R' is;

Length of Q'R' = 1 - (-1) = 1 + 1 =2

Therefore.

The scale factor for the dilation is;

$\rm Scale \ factor=\dfrac{Length \ of \ QR}{Length \ of \ Q'R'}\\\\Scale \ factor=\dfrac{6}{2}\\\\Scale \ factor=3$

Hence, the scale factor of a dilation is 3,

To know more about the Scale factor click the link given below.

https://brainly.com/question/24771289