Question

Type the correct answer in each box. Use numerals instead of words.

You reflect triangle PQR, with coordinates P(-4, -4), Q(-1, -3), and R(-3, -1), across the x-axis, across the y-axis, and across the x-axis again to form triangle P′Q′R′.

After these reflections, the coordinates of P′ will be (,

Answer 1

After these reflections, the coordinates of P′ will be (4 , -4)

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)

* Lets solve the problem

- The triangle PQR with coordinates P(-4, -4), Q(-1, -3), and R(-3, -1)

- The triangle is reflected across the x-axis

∵ Δ PQR is reflected across the x-axis

∴ All y-coordinates of the vertices P, Q , R reversed their signs

∴ The new points will be (-4 , 4) , (-1 , 3) , (-3 , 1)

- The new vertices will reflected across the y-axis

∴ All x-coordinates of the new vertices reversed their signs

∴ The new points will be (4 , 4) , (1 , 3) , (3 , 1)

- The new vertices will reflected across the x-axis to form Δ P'Q'R'

∴ All y-coordinates of the new vertices reversed their signs

∴ P' = (4 , -4) , Q' = (1 , -3) , R' = (3 , -1)

* After these reflections, the coordinates of P′ will be (4 , -4)