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Home » Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.
Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.
CBSE | Class 10 | Coordinate Geometry | Maths | NCERT
Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.

Solution: All three points are collinear if the total of the lengths of any two line segments equals the length of the third line segment.

Consider the following values, A = (1, 5) B = (2, 3) and C = (-2, -11)

Calculate the distance between three points, say AB, BC, and CA.

AB=\sqrt{{{\left( 2-1 \right)}^{2}}+{{\left( 3-5 \right)}^{2}}}=\sqrt{{{\left( 1 \right)}^{2}}+{{\left( -2 \right)}^{2}}}=\sqrt{1+4}=\sqrt{5}

BC=\sqrt{{{\left( -2-2 \right)}^{2}}+{{\left( -11-3 \right)}^{2}}}=\sqrt{{{\left( -4 \right)}^{2}}+{{\left( -14 \right)}^{2}}}=\sqrt{16+196}=\sqrt{212}

CA=\sqrt{{{\left( -2-1 \right)}^{2}}+{{\left( -11-5 \right)}^{2}}}=\sqrt{{{\left( -3 \right)}^{2}}+{{\left( -16 \right)}^{2}}}=\sqrt{9+256}=\sqrt{265}

As we know, AB + BC ≠ CA

As a result, the points given (1, 5), (2, 3), and ( – 2, – 11) are not collinear.

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