Question

If the points $A(0,6),B(2,1)$ and $C(7,3)$ are three corners of a square $ABCD$, then the slope of the diagonal $BD$ is

• A. $\frac{7}{3}$
• B. $-\frac{7}{3}$
• C. $\frac{5}{3}$
• D. $-\frac{3}{7}$

Answer 1

The correct option is A $\frac{7}{3}$

Slope of $AC$
$m_1=\frac{3-6}{7-0}=-\frac{3}{7}$
As we know, diagonals of square are perpendicular to each other.
$\therefore m_1\cdot m_2=-1\Rightarrow m_2=-\frac{1}{m_1}=\frac{7}{3}$

$\therefore$ Slope of $BD=\frac{7}{3}$