Question

 Rectangle PQRS has vertices P(1, 4), Q(6, 4), R(6, 1), and S(1, 1). Without graphing, find the new coordinates of the vertices of the rectangle after a reflection over the x-axis and then another reflection over the y-axis.
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Answer 1

The vertices of the rectangle after a reflection over the x-axis and then another reflection over the y-axis are:

P" (-1 , -4) , Q" (-6 , -4) , R" (-6 , -1) , S" (-1 , -1)

Step-by-step explanation:

Let us revise some transformation

• If point (x , y) reflected across the x-axis , then its image is (x , -y) , the rule of reflection is rx-axis (x , y) → (x , -y)
• If point (x , y) reflected across the y-axis , then its image is (-x , y) , the rule of reflection is ry-axis (x , y) → (-x , y)

∵ PQRS is a rectangle

∵ P = (1 , 4) , Q = (6 , 4) , R = (6 , 1) , S = (1 , 1)

∵ The rectangle is reflected across x-axis

- That means change the signs of the y-coordinates of all

   vertices of rectangle PQRS

∴ P' = (1 , -4) , Q' = (6 , -4) , R' = (6 , -1) , S' = (1 , -1)

∵ The rectangle P'Q'R'S' is reflected across the y-axis

- That means change the signs of the x-coordinates of all

   vertices of rectangle P'Q'R'S'

∴ P" = (-1 , -4) , Q" = (-6 , -4) , R" = (-6 , -1) , S" = (-1 , -1)

The vertices of the rectangle after a reflection over the x-axis and then another reflection over the y-axis are:

P" (-1 , -4) , Q" (-6 , -4) , R" (-6 , -1) , S" (-1 , -1)

Learn more:

You can learn more about the transformation in brainly.com/question/5563823

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