Which of the steps will cause the rectangle to map into ourself?

Answer with explanation:

 The coordinates of the given rectangle are:A (2,2),B(2,6),C(8,6) and D(8,2).

When you reflect the rectangle across X axis, The coordinates of Image rectangle are :A' (2,-2),B'(2,-6),C'(8,-6) and D'(8,-2).

The meaning of term reflection is that, distance of Preimage that is each vertex of Rectangle from X axis, is same from Image ,that is Distance of each corresponding vertex from X axis.

Now,we have to map the rectangle into Itself,

So, after reflecting through X axis, as x coordinate of Ordered pair are same.

So,→ y-coordinate of Image + Vertical Shift =  y-coordinate of Pre-Image

        ⇒ -2 + Vertical Shift = 2

⇒Vertical shift = 2 +2

⇒Vertical shift = 4 Units

Option D:

  Reflect across x-axis ,then shift 4 units up.

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.