Ineed 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′.

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)

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