Question

in the figure, mp is the perpendicular bisector of no. which transformation will prove △mnp≅△mop using the given information?
a) translation along np such that n lines up with p
b) rotation 90° counterclockwise about p
c) dilation with scale factor 1 about p
d) reflection over mp

Explanation:

Step1: Recall properties of transformations

Translation moves a figure, rotation turns a figure, dilation changes size, and reflection flips a figure over a line.

Step2: Analyze the given situation

Since $MP$ is the perpendicular bisector of $NO$, reflecting $\triangle MNP$ over $\overline{MP}$ will map $N$ to $O$ (because a perpendicular bisector has this property of reflection - related congruence). The two triangles $\triangle MNP$ and $\triangle MOP$ will coincide after reflection over $\overline{MP}$.

Answer:

D. reflection over $\overline{MP}$