Answer:
After these reflections, the coordinates of P' will be P'(4,-4)
Step-by-step explanation:
<u><em>The question is</em></u>
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)
