Answer:
The length of MN is 30.
Step-by-step explanation:
It is given that △XYZ maps to △MNO with the transformation
[tex](x,y)\rightarrow (5x,5y)[/tex]
This rule of transformation represents the dilation with scale factor 5 because the dilation about the origin is defined as
[tex](x,y)\rightarrow (kx,ky)[/tex]
where, k is scale factor.
In dilation, the image and preimage are similar and scale factor is the ratio of corresponding side of image and preimage.
In △XYZ and △MNO,
[tex]k=\frac{MN}{XY}[/tex]
[tex]5=\frac{MN}{6}[/tex]
Multiply both sides by 6.
[tex]30=MN[/tex]
Therefore the length of MN is 30.
