Question
If the vertices B and D of a square ABCD are \((2, 3)\) and \((4, 1)\) respectively, then what is the area of the square?
This question was previously asked in
NDA 2 2025 GAT Question Paper (14-Sep-2025)
The correct answer is
4 square units
To solve this problem, we need to determine the area of a square with vertices \( B \) and \( D \) given at coordinates \((2, 3)\) and \((4, 1)\) respectively. Let's follow these steps:
- Determine the distance between points \( B \) and \( D \), which can be considered as the diagonal of the square.
- Use the distance formula to calculate \( BD \): \( \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).
- Substitute the coordinates of \( B \) \((2, 3)\) and \( D \) \((4, 1)\) into the formula:
- In a square, the diagonal \( d \) is related to the side \( s \) by the equation \( d = s\sqrt{2} \). We can solve for the side \( s \) of the square:
- Thus, \( s = 2 \).
- Calculate the area of the square using the side length \( s \). The formula for the area \( A \) of a square is given by \( A = s^2 \).
Therefore, the area of the square is 4 square units. This matches option 1:
4 square units
.
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