Question

Show that the points (0,-2),(2,4)and (-1,5) are collinear

Answer 1

Answer:

the points will be collienar if they have the dividing ratio same or have slope same or the distance between them will be equal

A ( 0 , -2 ) and B ( 2 , 4 )

Here,

AB = ✓( 2 - 0 )² + ( 4 + 2 )²

AB = ✓4 + 36

AB = √40 = ✓2 × 2 × 2 × 5

AB = 2√10 units.

B ( 2 , 4 ) and C ( -1 ,5 )

BC = ✓ ( -1 - 2 )² + ( 5 - 4 )²

BC = ✓9 + 1

BC = ✓10

BC = √10

A ( 0 , -2 ) and C ( -1 , 5 )

AC = ✓ ( -1 - 0)² + ( 5 + 2 )²

AC = ✓1 + 49

AC=5√2 units

AB + AC = 2√10 + 5√2 not =3√10 units.

And,

BC = √10 units.

Thus,

The given points A , B , C are not collinear.

you can verify by using the slope of ab=slope of bc=slope of ca