Question

If the coordinates of opposite vertices of a square are $(1,3)$ and $(6,0)$, the length if a side of a square is

• A. $\sqrt{34}$
• B. $\sqrt{17}$
• C. $17$
• D. $12$

Answer 1

The correct option is B $\sqrt{17}$

The distance between points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

Let the length of one side of the square = a

$\therefore$ Length of the diagonal of square = $a\sqrt{2}$

$a\sqrt{2}$ $=$ $\sqrt{{(1-6)}^2+{(3-0)}^2}$

$=\sqrt{34}$

$=\sqrt{2}\cdot \sqrt{17}$

$\therefore a=\sqrt{17}$