Question

i need help with math 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′.

Answer 1

Answer:

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

Step-by-step explanation:

The question is

After these reflections, the coordinates of P' will be?

we have

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

Part 1) Reflect triangle PQR across the x-axis

we know that

The rule of the reflection of a point across the x-axis is

(x,y) -----> (x,-y)

Applying the rule of the reflection across the x-axis at the coordinates of triangle PQR

P(-4, -4) -----> P'''(-4,4)

Q(-1, -3) -----> Q'''(-1, 3)

R(-3, -1) ----> R'''(-3, 1)

Part 2) Reflect triangle P'''Q'''R''' across the y-axis

we know that

The rule of the reflection of a point across the y-axis is

(x,y) -----> (-x,y)

Applying the rule of the reflection across the y-axis at the coordinates of triangle P'''Q'''R'''

P'''(-4,4) -----> P''(4,4)

Q'''(-1, 3) ---> Q''(1, 3)

R'''(-3, 1) ---> R''(3, 1)

Part 3) Reflect triangle P''Q''R'' across the x-axis again

we know that

The rule of the reflection of a point across the x-axis is

(x,y) -----> (x,-y)

Applying the rule of the reflection across the x-axis at the coordinates of triangle P''Q''R''

P''(4,4) ---->  P'(4,-4)

Q''(1, 3) ----> Q'(1, -3)

R''(3, 1) ----> R'(3, -1)

therefore

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