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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′?

Respuesta :

Ashraf82

Answer:

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

sorry ignore this my answer was wrong and i have no clue how to delete this

its not x=0 if its reflected over the x-axis but it is x=0 if ur looking for the shape reflected over the y-axis. The question for both things are very similar the picture is the only difference sorry have  a nice day

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