Question

point f on the coordinate grid is reflected across a line to create point f. then, points e, f, and f are connected to create a triangle. kari says point e must be on the perpendicular bisector of the line ff, regardless of the line across which point f was reflected.

Explanation:

Step1: Recall reflection property

By the definition of reflection, a point and its reflection are equidistant from the line of reflection. The line of reflection is the perpendicular bisector of the segment connecting a point and its reflection, i.e., for point $F$ and its reflection $F'$, the line of reflection is the perpendicular bisector of $\overline{FF'}$.

Step2: Analyze point - line relationship

There is no information or reason given that would force point $E$ to be on the perpendicular bisector of $\overline{FF'}$. Point $E$ is an arbitrary point in the coordinate - plane and has no inherent connection to the line of reflection of point $F$ that would place it on the perpendicular bisector of $\overline{FF'}$.

Answer:

Kari's claim is false.