## TRIANGLE WORKSHEET SOLUTION 3

Triangle Worksheet Solution 3 :

In this section, you will have solutions for the problems on determining if the given points are collinear or not.

Determine if the following set of points are collinear or not.

(i)  (4,3) (1,2) and (-2,1)

Solution :

Let A (4,3) B (1,2) and C (-2,1) are the vertices of the triangle

If the three points are collinear then area of triangle will be zero

x₁ = 4          x₂ = 1         x₃ = -2

y₁ = 3          y₂ = 2         y₃ = 1 =  (1/2)[ (8 + 1 – 6) – (3 - 4 + 4) ]

=  (1/2)[ 3 – 3]

=  0

Hence, the given points are collinear.

(ii) (-2, -2) (-6, -2) and (-2, 2)

Solution :

Let A (-2,-2) B (-6,-2) and C (-2,2) are the vertices of the triangle

If the three points are collinear then area of triangle will be zero

x₁ = -2          x₂ = -6         x₃ = -2

y₁ = -2          y₂ = -2         y₃ = 2 =  (1/2)[ (4 - 12 + 4) – (12 + 4 - 4) ]

=  (1/2)[ - 4 – 12]

=  (1/2) (-16)

=  -8

Area of triangle is not equal to zero.

Hence the given points are not collinear.

(iii)   (-3/2, 3) (6, -2) and (-3, 4)

Solution :

Let A (-3/2,3) B (6,-2) and C (-3,4) are the vertices of the triangle

If the three points are collinear then area of triangle will be zero

x₁ = -3/2          x₂ = 6         x₃ = -3

y₁ = 3             y₂ = -2         y₃ = 4 =  (1/2) [(3 + 24 - 9) – (18 + 6 - 6)]

=  (1/2) [(27 - 9) - (18)]

=  (1/2) (18 - 18)

=  0

Hence the given points are collinear.

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