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
