The points (0, 5), (-2, -2), (5, 0) and (7, 7) are the vertices of a 

Concept:

Parallelogram:

• Opposite sides and opposite angles are equal.
• Digonals are not equal 

Rectangle:

• Rectangle is a parllelogram in which every angle is 90°

• Digonals are equal in lengths 

Rhombus: 

• It is a parallelogram in which all sides are equal
• Digonals are not equal in lengths

Square:

• All sides are equal and each angle is 90° 
• Diagonals are equal in lengths.

Distance between two points (x₁, y₁) and (x₂, y₂) is given by, \(\rm \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Calculation:

Let, the given points be A(0, 5), B(-2, -2), C(5, 0) and D(7, 7). Then ABCD is a quadrilateral in which:

AB, BC, CD, and DA are sides

AB = \(\sqrt{(-2-0)^2+(-2-5)^2}=\sqrt{(-2)^2+(-7)^2}=\sqrt{4+49}=\sqrt{53}\) units

BC = \(\sqrt{(5-(-2))^2+(0-(-2))^2}=\sqrt{(7)^2+(2)^2}=\sqrt{4+49}=\sqrt{53}\) units

CD = \(\sqrt{(7-5)^2+(7-0)^2}=\sqrt{(2)^2+(7)^2}=\sqrt{4+49}=\sqrt{53}\) units

DA = \(\sqrt{(0-7)^2+(5-7)^2}=\sqrt{(-7)^2+(-2)^2}=\sqrt{4+49}=\sqrt{53}\) units

Here, AB = BC = CD = DA , i.e., all sides are equal.

Now, AC and BD are diagonals of ABCD

\(\rm AC=\sqrt{(5-0)^2+(0-5)^2}=\sqrt{(5)^2+(-5)^2}=\sqrt{25+25}=\sqrt{50}=5\sqrt2\) units

And, \(\rm BD=\sqrt{(7-(-2))^2+(7-(-2))^2}=\sqrt{(9)^2+(9)^2}=\sqrt{81+81}=\sqrt{162}=9\sqrt2\) units

∴ AC ≠ BD ⇒ Digonals are not equal in length.

In ABCD, all sides are equal but digonals are not equal.

Thus, ABCD is a rhombus.

Hence, option (3) is correct.