Question

$A(0,0),B(7,2),C(7,7)$ and $D(2,7)$ are the vertices of a quadrilateral. The respective slopes of diagonals $AC$ and $BD$ are

• A. $-1,1$
• B. $1,-1$
• C. $0,-1$
• D. $1,0$

Answer 1

The correct option is B $1,-1$

The slope of a line passing through the point $(x_1,y_1)$ and $(x_2,y_2)$ is given by

$m=\frac{y_2-y_1}{x_2-x_1}$
Given : $A(0,0),B(7,2),C(7,7)$ and $D(2,7)$ are the vertices of quadrilateral

$AC$ and $BD$ are diagonals of a quadrilateral

Then, slope of diagonal $AC$ is
$m_{AC}=\frac{7-0}{7-0}$
$⟹m_{AC}=\frac{7}{7}$
$\therefore m_{AC}=1$
Similarly, slope of $BD$ is

$m_{BD}=\frac{7-2}{2-7}$
$⟹m_{BD}=\frac{5}{-5}$
$\therefore m_{BD}=-1$.

Hence, the slopes of diagonals $AC$ and $BD$ are $1$ and $-1$ respectively.