Pentagon pqrst and its reflection, pentagon p′q′r′s′t′, are shown in the coordinate plane below: pentagon pqrst and pentagon p prime q prime r prime s prime t prime on the coordinate plane with ordered pairs at p negative 4, 6, at q negative 7, 4, at r negative 6, 1, at s negative 2, 1, at t negative 1, 4, at p prime negative 4, negative 6, at q prime negative 7, negative 4, at r prime negative 6, negative 1, at s prime negative 2, negative 1, at t prime negative 1, negative 4 what is the line of reflection between pentagons pqrst and p′q′r′s′t′?

The line of reflection between pentagons PQRST and P′Q′R′S′T′ is

the x-axis

Step-by-step explanation:

* Lets revise some transformation

- If point (x , y) reflected across the x-axis

 ∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

 ∴ Its image is (-x , y)

- If point (x , y) reflected across the line y = x

 ∴ Its image is (y , x)

- If point (x , y) reflected across the line y = -x

 ∴ Its image is (-y , -x)

* Lets solve the problem

∵ The vertices of the polygon PQRST are

  P = (-4 , 6) , Q = (-7 , 4) , R = (-6 , 1) , S = (-2 , 1) , T = (-1 , 4)

∵ The vertices of the polygon P'Q'R'S'T' are

  P' = (-4 , -6) , Q' = (-7 , -4) , R' = (-6 , -1) , S' = (-2 , -1) , T' = (-1 , -4)

- By comparing the vertices with their images, all y-coordinates

 have opposite sign in the images

∵ The signs of the y-coordinates in all vertices are changed

∵ The reflection of a point across the x-axis change the sign of the

   y-coordinate

∴ polygon P'Q'R'S'T' is the image of polygon PQRST after reflection

  across the x-axis

* The line of reflection between pentagons PQRST and P′Q′R′S′T′ is

  the x-axis