Chelsea and anika trying to determine whether triangle abc and triangle pqr can be proven congruent through rigid motions chelsea says that triangle abc is congruent to triangle prq because triangle abc can be rotated 270 degrees clockwise to create triangle prq. anika says that triangle abc is congruent to triangle prq because triangle abc can be reflected over the x axis to create triangle prq. who is correct? i need the answer asap

Anika is correct

Step-by-step explanation:

* Lets revise the rules of reflection and rotation

- If point (x , y) reflected across the x-axis  then its image is (x , -y)

- If point (x , y) rotated about the origin by angle 270° clock wise  then

 its image is (-y , x)

* Lets check the vertices of the two triangles

- The vertices of Δ ABC are:

# A (-7 , 2)

# B (-3 , 6)

# C (-2 , 1)

- The vertices of Δ PRQ

# P (-7 , -2)

# R (-3 , -6)

# Q (-2 , -1)

* By comparing between the vertices of the two triangles

∵ Each y-coordinates of Δ PRQ has opposite sign of each

   y-coordinates of Δ ABC

∵ All x-coordinates of Δ PRQ are the same with x-coordinates of

  Δ ABC

- That means Δ PRQ is the image of Δ ABC after reflection across

  the x-axis  

∵ Reflection doesn't change the shape and the size of the figure

∴ Δ ABC and Δ PRQ have same size (equal sides and equal angles)

∴ Δ ABC is congruent to Δ PRQ

* Anika is correct

the correct answer is 5 6 and 7