Question

The four points (1,7), (4,2), (-1,-1), (-4,4) form a:

• A. Trapezium
• B. Rhombus
• C. Square
• D. Rectangle

Hint:

All sides equal $\implies$ Rhombus. Diagonals also equal $\implies$ Square.

Answer 1

The Correct Option is C

Step 1: Concept
Properties of quadrilaterals using distance formula.

Step 2: Analysis
Calculate side lengths between consecutive points.
$AB = \sqrt{(4-1)^2 + (2-7)^2} = \sqrt{9+25} = \sqrt{34}$. All sides equal $\sqrt{34}$.

Step 3: Calculation
Calculate diagonals: $AC = \sqrt{(-1-1)^2 + (-1-7)^2} = \sqrt{4+64} = \sqrt{68}$.
$BD = \sqrt{(-4-4)^2 + (4-2)^2} = \sqrt{64+4} = \sqrt{68}$. Diagonals are equal.

Step 4: Conclusion
Since all sides are equal and diagonals are equal, it is a square. Final Answer: (C)