Answer:
The scale factor was 3
Step-by-step explanation:
we know that
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(0,2) and B(2,3) -----> see the figure
substitute in the formula
[tex]d=\sqrt{(3-2)^{2}+(2-0)^{2}}[/tex]
[tex]d=\sqrt{(1)^{2}+(2)^{2}}[/tex]
[tex]AB=\sqrt{5}\ units[/tex]
step 2
Find the distance A'B'
we have
A'(0,6) and B'(6,9) -----> given value
substitute in the formula
[tex]d=\sqrt{(9-6)^{2}+(6-0)^{2}}[/tex]
[tex]d=\sqrt{(3)^{2}+(6)^{2}}[/tex]
[tex]A'B'=\sqrt{45}\ units[/tex]
simplify
[tex]A'B'=3\sqrt{5}\ units[/tex]
step 3
Find the scale factor
To find out the scale factor divide the length of the image A'B' by the length of the pre-image AB
so
[tex]3\sqrt{5}/\sqrt{5}=3[/tex]
therefore
The scale factor was 3
