reflection and translation.
Given:
The different transformation in the options.
To find:
The transformation that would result in the perimeter of a triangle being different from the perimeter of its image.
Solution:
In option 1,
It represents reflection across the line y=x.
In option 2,
It represents reflection across the x-axis.
In option 3,
It represents dilation by scale factor 4 and the center of dilation is at origin.
In option 4,
It represents translation 2 units right and 5 units down.
We know that the reflection and translation are rigid transformations, It means the size and shape of the figure remains the same after transformation.
So, the perimeter of the figure and its image are same in the case of reflection and translation.
But dilation is not a rigid transformation. In dilation, the figure is similar to its image. So, the perimeter of the figure and its image are different in the case of dilation.
Therefore, the correct option is 3.