In this page triangle worksheet solution3 we are going to see solution for each problems of the topic area of triangle worksheet.

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

Therefore 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.Therefore 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

Therefore the given points are collinear.

triangle worksheet solution3 triangle worksheet solution3

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