In the given diagram, we want to identify the transformation that maps △HGF onto △KJN.
The transformation is not a translation because we cannot map △HGF onto △KJN by just moving △HGF while maintaining its orientation. Moreover, the transformation is not a reflection because there is no line of symmetry between △HGF and △KJN. This mapping looks like a rotation.
Writing the Rule
Let's start by finding the center of rotation. To do so, we will connect with line segments the corresponding vertices of the preimage and image. The point of intersection of these segments will be the center of rotation.
The point (0,2) is the center of rotation. The angle of rotation seems to be 180^(∘). Recall that unless we are specifically told otherwise, rotations are performed counterclockwise. Let's confirm these two things!
We can see that the transformation that maps △HGF onto △KJN is a rotation 180^(∘) about point (0,2). This can be written as r_((180^(∘), (0,2)))( △HGF)= △KJN.
