Question

The points A(1, 1), B(3, 2) and C(5, 3) cannot be the vertices of the triangle ABC. Justify.​

Answer 1

Answer:

The points A(1, 1), B(3, 2) and C(5, 3) cannot be the vertices of the triangle ABC.

Step-by-step explanation:

In the context to the question;

we have to find that  the vertices provided cannot be the vertices of triangle;

given;

A(1, 1),

B(3, 2)

C(5, 3)

Now we know that ;

Area of triangle = 1/2 [ x₁(y₂-y₃)+ x₂(y₃-y₁)+ x₃(y₁-y₂)]

here we know;

(x₁,y₁)=[1;1]

(x₂,y₂)= [3;2]

(x₃,y₃)= [5;3]​

now by putting the value in the formula;

Area of triangle = 1/2 [ 1(2-3)+ 3(3-1)+ 5(1-2)]

= 1/2 [ 1 (-1) +3(2)+5(-1)]

=1/2 [ -1 +6-5 ]

=1/2[ 0 ]  

=0 sq. unit

the area of the triangle is 0

So we can conclude that the points A(1, 1), B(3, 2) and C(5, 3) cannot be the vertices of the triangle ABC.

Answer 2

Answer:0

Step-by-step explanation:

In the context to the question;

we have to find that  the vertices provided cannot be the vertices of triangle;

given;

A(1, 1),

B(3, 2)

C(5, 3)

Now we know that ;

Area of triangle = 1/2 [ x₁(y₂-y₃)+ x₂(y₃-y₁)+ x₃(y₁-y₂)]

here we know;

(x₁,y₁)=[1;1]

(x₂,y₂)= [3;2]

(x₃,y₃)= [5;3]​

now by putting the value in the formula;

Area of triangle = 1/2 [ 1(2-3)+ 3(3-1)+ 5(1-2)]

= 1/2 [ 1 (-1) +3(2)+5(-1)]

=1/2 [ -1 +6-5 ]

=1/2[ 0 ]  

=0 sq. unit

the area of the triangle is 0

So we can conclude that the points A(1, 1), B(3, 2) and C(5, 3) cannot be the vertices of the triangle ABC.