Question

the diagram shows △rft and △rft. △rft is a transformation of △rft. which single transformation was applied to △rft to create △rft? reflection over the line pk clockwise rotation of 90° around point h counterclockwise rotation of 180° around point d translation of 3 units to the right and 5 units down.

Explanation:

Step1: Analyze reflection

If it was a reflection over the line $PK$, the orientation of the triangle would change in a mirror - like way across the line $PK$. Looking at the two triangles $\triangle RFT$ and $\triangle R'F'T'$, we can see that the corresponding points of the two triangles are equidistant from the line $PK$ and have the mirror - image property.

Step2: Analyze rotation

A $90^{\circ}$ clockwise rotation around point $H$ would change the orientation of the triangle in a way that is not consistent with what is shown. A $180^{\circ}$ counter - clockwise rotation around point $D$ would also not result in the given transformation as the orientation and position of the vertices relative to the center of rotation $D$ do not match.

Step3: Analyze translation

A translation of 3 units to the right and 5 units down would move all points of the triangle in a parallel fashion without any flipping or rotation. But the given transformation shows a flip, so translation is not correct.

Answer:

A. reflection over the line $PK$