Question

(6) Show that the points (8.1). (3.-4) and (2.-5)
are collinear​

Answer 1

Answer:

Since the given points are collinear, they do not form a

triangle, which means area of the triangle is Zero.

Area of a triangle with vertices (x

1

,y

1

) ; (x

2

,y

2

) and (x

3

,y

3

) is

∣

∣

∣

∣

2

x

1

(y

2

−y

3

)+x

2

(y

3

−y

1

)+x

3

(y

1

−y

2

)

∣

∣

∣

∣

Hence, substituting the points (x

1

,y

1

)=(8,1) ; (x

2

,y

2

)=(k,−4) and (x

3

,y

3

)=(2,−5)

the area formula, we get

∣

∣

∣

∣

2

8(−4+5)+k(−5−1)+2(1+4)

∣

∣

∣

∣

=0

=>8−6k+10=0

=>6k=18

=>k=3

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