Question

find the value of "k" for which the point p(-1,3),q(2,k) and r(5,-1) are collinear​

Answer 1

Answer:

Let A(−1,3), B(2,p) and C(5,−1) be the given points.

Three points are collinear if x

1

(y

2

−y

3

)+x

2

(y

3

−y

1

)+x

3

(y

1

−y

2

)=0

Therefore, x

1

(y

2

−y

3

)+x

2

(y

3

−y

1

)+x

3

(y

1

−y

2

)=0

⇒−1(p−(−1))+2(−1−3)+5(3−p)=0

⇒−1(p+1)+2(−4)+5(3−p)=0

⇒−p−1−8+15−5p=0

⇒−6p+6=0

⇒−6p=−6

⇒p=1

Hence p=1