Question

the points a(3,2) b(1,1) c(5 ,3) cannot be verticles of the triangle abc . justify​

Answer 1

SOLUTION :-

Given,

a = ( 3 , 2 )

b = ( 1 , 1 )

c = ( 5 , 3 )

Here,

$\bullet \sf \ x_1=3 \ , \ y_1=2 \\\\\bullet \ x_2=1 \ , \ y_2=1 \\\\\bullet \ x_3=5 \ , \ y_3= 3$

 $\boxed{\bf Area \ of \ triangle =\dfrac{1}{2} \times [ x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]}$

 $\longrightarrow\sf \dfrac{1}{2}\times [ 3\times(2-3)+1\times (3-1)+5\times( 2-1)]\\\\\longrightarrow \dfrac{1}{2} \times [(3\times -1)+2+(5\times 1)]\\\\\longrightarrow \dfrac{1}{2}\times [-3+2+5]\\\\\longrightarrow \dfrac{1}{2} \times [-5+5]\\\\\longrightarrow \dfrac{1}{2}\times 0 \\\\\longrightarrow 0$

Area of a triangle cannot be zero.

∴ The points a( 3, 2 ), b( 1 , 1 ) and c( 5 , 3 ) cannot be the vertices of the

    triangle abc.