Question

given that point p is the centroid of △mce, which of the following is true? additional information ct = 45.6 ne = nc ne = te two of these pt⊥pn

Explanation:

Step1: Recall centroid property

The centroid of a triangle divides each median in a 2:1 ratio. A median of a triangle is a line - segment joining a vertex to the mid - point of the opposite side. In $\triangle MCE$, if $P$ is the centroid and $CN$ is a median (assuming $N$ is the mid - point of $ME$), then by the definition of a median, the mid - point $N$ of side $ME$ implies that the distance from $N$ to $E$ is equal to the distance from $N$ to $M$. Also, since $N$ is the mid - point of $ME$, we have $NE=NC$ (because $N$ is the mid - point of the side opposite to vertex $C$ in $\triangle MCE$). There is no information to suggest that $NE = TE$ or that $\overline{PT}\perp\overline{PN}$.

Answer:

A. $NE = NC$