Prove that the points (- 2, 5), (0, 1) and (2, - 3) are collinear.
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Given : Points (- 2, 5), (0, 1) and (2, - 3)
To prove : Given points are collinear.
Solution :
Let A(- 2, 5), B(0, 1) and C(2, - 3) are the vertices
By using distance formula : √(x2 - x1)² + (y2 - y1)²
Vertices : A(- 2, 5), B(0, 1)
Length of side AB = √(0 + 2)² + (1 - 5)²
AB = √2² + (4)²
AB = √4 + 16
AB = √20
AB= √(5 × 4)
AB = 2√5 units
Vertices : B(0, 1) and C(2, - 3)
Length of side BC = √( 2 - 0)² + (- 3 - 1)²
BC = √(2)² + (-4)²
BC = √4 + 16
BC = √20
BC = √(5 × 4)
BC = 2√5 units
Vertices : A(- 2, 5), C(2, - 3)
Length of side AC = √(2 + 2)² + (- 3 - 5)²
AC = √(4)² + (-8)²
AC = √16 + 64
AC = √80 units
AC = √(16 × 5)
AC = 4√5 units
Since the length of AB + BC = AC , 2√5 + 2√5 = 4√5
Hence the points are collinear.
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