Question

Show that the points (–1, 7), (3, –5) and (4, –8) are collinear.​

Answer 1

Let A ( −1 , 7 ) , B ( 3 , −5 ) , C ( 4 , −8 ) be the coordinates.

The given points are said to be collinear if area of △ ABC = 0.

$\triangle=$ 1 / 2 | -1   7    1 |       { small straight lines are determinants}

              | 3   -5   1 |

              | 4   -8   1 |

Expanding along first row ;

Δ = 1 /2 [ −1 ( −5 + 8 ) − 7 ( 3 − 4 ) + 1 ( −24 + 20 ) ]

Δ = 1 /2  [−1 (3) −7 (−1) + 1 (−4) ]

Δ= 1/2 [−3+7−4 ]

Δ = 0

As, the determinant results out to be zero, hence, the points are collinear.

Hope it helps.

Thank u.

Answer 2

Let A ( −1 , 7 ) , B ( 3 , −5 ) , C ( 4 , −8 ) be the coordinates.

The given points are said to be collinear if area of △ ABC = 0.

\triangle=△= 1 / 2 | -1 7 1 | { small straight lines are determinants}

| 3 -5 1 |

| 4 -8 1 |

Expanding along first row ;

Δ = 1 /2 [ −1 ( −5 + 8 ) − 7 ( 3 − 4 ) + 1 ( −24 + 20 ) ]

Δ = 1 /2 [−1 (3) −7 (−1) + 1 (−4) ]

Δ= 1/2 [−3+7−4 ]

Δ = 0

As, the determinant results out to be zero, hence, the points are collinear.

Hope it helps.

Thank u.

yes I am a srichaitanya student

u from which branch