Question

find the value of p for which the point (-1,3),(2,p) & (5,-1) are collinear.

Answer 1

Given that (-1,3),(2,p),(5,-1) are collinear
x1=-1 , x2=2 , x3=5 , y1=3 , y2=p , y3= -1
⇒ Area of triangle formed by these points = 0
⇒ 1/2[x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)] = 0
⇒ 1/2{[-1][p - (-1)} + 2[-1 - 3] + 5(3 - p)} = 0
⇒ 1/2{[-1][p+1] + 2[-4] + 15 - 5p} = 0
⇒ { -p - 1 +[-8] +15 - 5p } = 0×2
⇒ { -p - 1 - 8 +15 - 5p } = 0
⇒ { -6p -9 + 15 } = 0
⇒ { -6p +6 } = 0
⇒ -6p = -6
⇒ 6p = 6
⇒ p =6/6
∴ p =1
Hope you will understand this