Question

6.
Verify whether the points (-2,3), (4,2) and (10,1) are collinear or not.
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Answer 1

Step-by-step explanation:

Given :-

The points (-2,3), (4,2) and (10,1)

To find:-

Verify whether the points (-2,3), (4,2) and (10,1) are collinear or not?

Solution:-

Given points are (-2,3), (4,2) and (10,1)

Let (x1, y1)=(-2,3)=>x1 = -2 and y1 = 3

Let (x2, y2)=(4,2)=>x2=4 and y2=2

Let (x3, y3)=(10,1)=>x3=10 and y3= 1

We know that

If The area of a triangle formed by the given points (x1, y1),(x2, y2) and (x3, y3) is equal to zero then they are collinear points.

The area of a triangle is

∆= (1/2) |x1(y2-y3)+x2(y3-y1)+x3(y1-y2) | sq.units

On Substituting these values in the above formula

=>(1/2) |(-2)(2-1)+4(1-3)+10(3-2) |

=> (1/2) | (-2)(1)+4(-2)+10(1) |

=> (1/2) | -2-8+10 |

=> (1/2) | -10+10 |

=> (1/2) | 0 |

=> 0/2

=> 0 sq.units

Area of the triangle formed by the given points is

0 sq.units

They are Collinear points

Answer:-

The given points for the given problem are Collinear Points

Used formulae:-

• If The area of a triangle formed by the given points (x1, y1),(x2, y2) and (x3, y3) is equal to zero then they are collinear points.The area of a triangle is
• ∆= (1/2) |x1(y2-y3)+x2(y3-y1)+x3(y1-y2) | sq.units