Question

The points $X(-1,3),Y(8,-3)$ and $Z(2,1)$

• A. are collinear
• B. not decided
• C. cannot be plotted
• D. are not collinear

Answer 1

Answer: (A)

are collinear

Three points $A(x_1,y_1,B(x_2,y_2)$ and $C(x_3,y_3)$ are said to be col-linear if $slope{m}_{AB}=slope{m}_{BC}=slope{m}_{AC}$

We know that, the slope of a line passing through the points $(x_1,y_1)\&(x_2,y_2)$ is

$m=\frac{y_2-y_1}{x_2-x_1}.$

Given , $X(-1,3),Y(8,-3),Z(2,1)$
$m_{XY}=\frac{-3-3}{8+1}$

$=\frac{-6}{9}$$=\frac{-2}{3}$

$m_{YZ}=\frac{1+3}{2-8}$

$=\frac{4}{-6}$$=\frac{-2}{3}$

$m_{XZ}=\frac{1-3}{2+1}$
$=\frac{-2}{3}$
$⟹m_{XY}=m_{YZ}=m_{XZ}$
Hence, three points are collinear.