PLEASE I NEED HELP ASAP

The question is :
Danielle reflects shape S in the line x = - 1 , and then reflects the new shape in the line y = 2

Zachary reflects shape S in the line y = 2 , and then reflects the new shape in the line x = - 1

Work out the coordinates of the vertex that A maps to after

a) Danielle's two reflections.

b) Zachary's two reflections.
.

The coordinates of the vertex that A maps to after Daniel's reflections are (3, 4) and the coordinates of the vertex that A maps to after Zachary's reflections are (3, 2)

How to determine the coordinates of the vertex that A maps to after the two reflections?

From the given figure, the coordinate of the vertex A is represented as:

A = (-5, 2)

The coordinates of the vertex that A maps to after Daniel's reflections

The rule of reflection across the line x = -1 is

(x, y) ⇒ (-x - 2, y)

So, we have:

A' = (5 - 2, 2)

Evaluate the difference

A' = (3, 2)

The rule of reflection across the line y = 2 is

(x, y) ⇒ (x, -y + 4)

So, we have:

A'' = (3, -2 + 4)

Evaluate the difference

A'' = (3, 4)

Hence, the coordinates of the vertex that A maps to after Daniel's reflections are (3, 4)

The coordinates of the vertex that A maps to after Zachary's reflections

The rule of reflection across the line y = 2 is

(x, y) ⇒ (x, -y + 4)

So, we have:

A' = (-5, -2 + 4)

Evaluate the difference

A' = (-5, 2)

The rule of reflection across the line x = -1 is

(x, y) ⇒ (-x - 2, y)

So, we have:

A'' = (5 - 2, 2)

Evaluate the difference

A'' = (3, 2)

Hence, the coordinates of the vertex that A maps to after Zachary's reflections are (3, 2)