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