Question

. The points A(1, 1), B(3, 2) and C15, 3) cannot be the vertices of the
triangle ABC Justify.​

Answer 1

Answer:

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

To Find : Show that points can not be the vertices of the triangle ABC.

Step-by-step explanation:

Solution :

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

Slope of AB = (2 - 1)/(3 - 1) = 1/2

Slope of AC = (3-1)/(5-1) = 2/4 = 1/2

Slope of BC = (3 - 2)/(5-3) = 1/2

Slope is same hence all points are collinear

so they can not be vertices of triangle

Another way

Area = (1/2) | 1( 2- 3) + 3(3 - 1) + 5(1 - 2) |

= (1/2) | -1 + 6 - 5 |

= (1/2) | 0 |

= 0

Area is zero hence can not be vertices of triangle

Another way

AB = √((3-1)² + (2-1)² ) = √5

BC = √((5-3)² + (3-2)² ) = √5

AC = √((5-1)² + (3-1)² ) = √20 = 2√5

√5 + √5 = √5

AB + BC = AC ( Sum of any two sides should be greater than third side not satisfied)

hence can not be vertices of triangle

THANKS❤