Question

plz give me the answer​

Answer 1

the points are collinear.......

NOTE:- if u don't believe u can check by marking points on a graph paper

DON'T FORGET TO MARK IT AS THE BRAINLIEST............

Answer 2

Given :

Points : A(1 , -3) , B(2 , -5) , C(-4 , 7) .

To determine :

Whether the given points are collinear .

Approach 1 :

Using distance formula :

• Note : The distance between the points A(x1 , y1) and B(x2 , y2) is given by ;

AB = √ [ (x2 - x1)² + (y2 - y1)² ]

Thus ,

The distance between points A(1 , -3) and B(2 , -5) will be ;

=> AB = √[ (2 - 1)² + (-5 + 3)² ]

=> AB = √[ 1² + (-2)² ]

=> AB = √[ 1 + 4 ]

=> AB = √5

Also ,

The distance between points B(2 , -5) and C(-4 , 7) will be ;

=> BC = √[ (-4 - 2)² + (7 + 5)² ]

=> BC = √[ (-6)² + (12)² ]

=> BC = √[ 36 + 144 ]

=> BC = √180

=> BC = 6√5

Also ,

The distance between points A(1 , -3) and C(-4 , 7) will be ;

=> AC = √[ (-4 - 1)² + (7 + 3)² ]

=> AC = √[ (-5)² + (10)² ]

=> AC = √[ 25 + 100 ]

=> AC = √125

=> AC = 5√5

Now ,

=> AB + AC = √5 + 5√5

=> AB + AC = 6√5

=> AB + AC = BC

=> The points A , B and C are collinear .

[ Note : From the equation AB + AC = BC , we can conclude that point A lies between points B and C . ]

Approach 2 :

Using slope of straight line :

• Note : The slope of the line joining the points A(x1 , y1) and B(x2 , y2) is given by ;

Slope of AB = (x2 - x1) / (y2 - y1)

Thus ,

The slope of line segment joining the points A(1 , -3) and B(2 , -5) will be ;

=> Slope of AB = (-5 + 3)/(2 - 1)

=> Slope of AB = -2/1

=> Slope of AB = -2

Also ,

The slope of line segment joining the points A(1 , -3) and C(-4 , 7) will be ;

=> Slope of AC = (7 + 3)/(-4 - 1)

=> Slope of AC = 10/-5

=> Slope of AC = -2

Clearly ,

Slope of AB = Slope of AC .

Thus ,

The points A , B and C are collinear .

Approach 3 :

Using area of triangle :

• Note : The area of the triangle formed by the points A(x1 , y1) , B(x2 , y2) and C(x3 , y3) is given by ;

∆ = ½•| x1(y2-y3) + x2(y3-y1) + x3(y1-y2) |

Thus ,

The area of triangle formed by the points A(1 , -3) , B(2 , -5) and C(-4 , 7) will be ;

=> ∆ = ½•| 1(-5-7) + 2(7+3) + (-4)(-3+5) |

=> ∆ = ½•| 1•(-12) + 2•10 + (-4)•2 |

=> ∆ = ½•| -12 + 20 - 8

=> ∆ = ½•| 20 - 20 |

=> ∆ = ½•| 0 |

=> ∆ = ½•0

=> ∆ = 0

Since the area of the triangle formed by the points A , B and C is zero , thus the points A , B and C are collinear .