Answer:
The scale factor is 2.5
Step-by-step explanation:
we know that
A dilation is a non rigid transformation that produce similar figures
If two figures are similar then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor
Let
z ---> the scale factor
so
[tex]z=\frac{A'B'}{AB}=\frac{B'C'}{BC}=\frac{A'C'}{AC}[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
step 1
Find the distance AB
we have
A(0,0) B(0,4)
substitute
[tex]d=\sqrt{(4-0)^{2}+(0-0)^{2}}[/tex]
[tex]d=\sqrt{(4)^{2}+(0)^{2}}[/tex]
[tex]AB=4\ units[/tex]
step 2
Find the distance A'B'
we have
A'(0,0) B'(0,10)
substitute
[tex]d=\sqrt{(10-0)^{2}+(0-0)^{2}}[/tex]
[tex]d=\sqrt{(10)^{2}+(0)^{2}}[/tex]
[tex]A'B'=10\ units[/tex]
step 3
Find the scale factor
[tex]z=\frac{A'B'}{AB}[/tex]
substitute the values
[tex]z=\frac{10}{4}=2.5[/tex]
therefore
The scale factor is 2.5 ( is an enlargement)
