Answer:
2). B
Step-by-step explanation:
We have been given a triangle ABC, whose midpoints are M, N and O. We are asked to complete the given transformation.
[tex]H_M{\circ}H_O:C\rightarrow[/tex]
The midpoint theorem states that segment connecting the midpoints of two sides of a triangle is parallel to third side and half the measure of third side. By midpoint theorem:
[tex]\overline{MN}=\overline{AO}=\overline{OC}[/tex]
[tex]\overline{ON}=\overline{AM}=\overline{MB}[/tex]
[tex]\overline{MO}=\overline{BN}=\overline{NC}[/tex]
We can see that by joining midpoints, we get 4 congruent triangles:
[tex]\Delta MN\cong \Delta MAO\cong \Delta ONM \cong \Delta NOC[/tex]
We can also see that midpoint M corresponds to vertex C, so midpoint O will correspond to vertex B.
Therefore our required transformation would be [tex]H_M{\circ}H_O:C\rightarrow B[/tex] and 2nd option is the correct choice.
