Question

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

Answer 1

Step-by-step explanation:

Given :-

The points A ( 1, 1 ), B ( 3, 2 ) and C ( 5,3)

To find:-

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

Solution:-

Given points are :-

A ( 1, 1 ), B ( 3, 2 ) and C ( 5,3 )

Let (x1, y1) = (1,1)=>x1 = 1 and y1 = 1

Let (x2, y2)=(3,2)=>x2=3 and y2=2

Let (x3, y3)=(5,3)=>x3=5 and y3=3

We know that

Area of a triangle whose vertices are( x1, y1), (x2, y2) ,(x3, y3) is

∆=(1/2) |x1(y2-y3)+x2(y3-y1)+x3(y1-y2) | sq.units

=>∆=(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) | 6-6 |

=>∆=(1/2) |0 |

=>∆=0/2

=>∆=0 sq.units

Area of a triangle formed by these points is 0 sq.units

So, They are collinear points

The triangle can not be formed by these points

Answer:-

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

Used formulae:-

• Area of a triangle whose vertices are( x1, y1), (x2, y2) ,(x3, y3) is

∆=(1/2) |x1(y2-y3)+x2(y3-y1)+x3(y1-y2) | sq.units

• The area of a triangle formed by the given points is zero then the points are called collinear points .
• If A,B,C are collinear then the area of a triangle formed by them is zero.
• AB+BC =AC then they are collinear points

Answer 2

Answer:

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