Question

carolina drew X'Y' 12 units long on a coordinate plane. Her dilated line segment is parallel to XY, which measures 15 units long. What was the scale factor of dilation for the line segment Carolina drew?

Answer 1

We are given

original line =XY=15 units

dilated line =X'Y'=12 units

now, we have to find dilated factor

we know that

dilated factor = (dilated line)/(original line)

Let's assume

dilated factor=D

so, we get

$D=\frac{X'Y'}{XY}$

we can plug value

and we get

$D=\frac{12}{15}$

now, we can simplify it

so, we can factor numerator and denominator

$D=\frac{3*4}{3*5}$

3 will get cancelled

$D=\frac{4}{5}$

so, dilated factor is

$=\frac{4}{5}$...............Answer

Answer 2

Dilation is the transformation of an object that resizes the object. The scale factor of dilation for the line segment Carolina drew is $\dfrac{4}{5}$.

What is dilation?

Dilation is the transformation of an object that resizes the object. The scale factor of a dilation is given as,

$\rm Scale\ factor =\dfrac{Dilated\ size}{Original\ size}$

We know that dilation is resizing, as we know that the original size of the line that Carolina drew was 12 units while the dilated size was 15 units. Thus, the scale ratio of the dilation of the line can be written as,

$\rm Scale\ factor =\dfrac{Dilated\ size}{Original\ size}$

$\rm Scale\ factor =\dfrac{12}{15}$

                  $=\dfrac{4}{5}$

Hence, the scale factor of dilation for the line segment Carolina drew is $\dfrac{4}{5}$.

Learn more about Dilation:

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