By using the perimeter formula for an orthogonally oriented rectangle set on a Cartesian plane, we find that the perimeter of the figure is 68/3 units.
In this question we have a rectangle oriented with respect to the two orthogonal axes of a Cartesian plane. In this case, the vertices of the figure are of the form:
A(x, y) = (a, b), B(x, y) = (c, b), C(x, y) = (a, d), D(x, y) = (c, d)
And the perimeter of this rectangle is equal to this:
p = 2 · |a - c| + 2 · |b - d|
If we know that a = - 5, b = 2, c = 2, d = - 7/3, then the perimeter of the rectangle is:
p = 2 · |- 5 - 2| + 2 · |2 - (- 7/3)|
p = 14 + 26/3
p = 68/3
By using the perimeter formula for an orthogonally oriented rectangle set on a Cartesian plane, we find that the perimeter of the figure is 68/3 units.
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