Question

A) draw the image of PQR after a 180 about the origin. Label the image P'Q'R

B) then reflect P'Q'R across the x-axis. label the image P''Q''R.

Answer 1

1- When rotating a figure 180 degrees around the origin (As it does not matter whether you move clockwise or counter-clockwise), we apply the rule (x, y) → (-x, -y).

Co-ordinates of the vertices,

P = (1, -1)

Q = (3, -2)

R = (3, -4)

And then calculating the co-ordinates of P', Q', R'

P' = (-1, 1)

Q' = (-3, 2)

R' = (-3, 4)

2- When reflecting a figure across X-axis, we apply the rule (x, y) → (x, -y).

Co-ordinates of the vertices,

P' = (-1, 1)

Q' = (-3, 2)

R' = (-3, 4)

And then calculating the co-ordinates of P'', Q'', R''

P'' = (-1, -1)

Q'' = (-3, -2)

R'' = (-3, -4)