Answer:
Scale factor to transform rectangle A into rectangle B is [tex]\frac{1}{3}[/tex].
Explanation:
If both rectangles are similar, then scale factor for width ([tex]r_{w}[/tex]) and height ([tex]r_{h}[/tex]), no unit, must be the same. That is:
[tex]r_{w} = r_{h}[/tex] (1)
[tex]\frac{w_{A}}{w_{B}} = \frac{h_{A}}{h_{B}}[/tex]
Where:
[tex]w_{A}, w_{B}[/tex] - Widths of rectangles A and B, no unit.
[tex]h_{A}, h_{B}[/tex] - Heights of rectangles A and B, no unit.
Let suppose that width is parallel to x-axis, whereas height is to y-axis. If we know that [tex]w_{A} = 3[/tex], [tex]w_{B} = 1[/tex], [tex]h_{A} = 6[/tex] and [tex]h_{B} = 2[/tex], then we have the following result:
[tex]\frac{3}{1} = \frac{6}{2}[/tex]
[tex]3 = 3[/tex]
Which algraically consistent and hence we conclude that scale factor to transform rectangle A into rectangle B is [tex]\frac{1}{3}[/tex].
