Question

if the points (k 3k) (3k 3k) and (3 1) are collinear find the value of k​

Answer 1

Step-by-step explanation:

Since the given points are collinear, they do not form a triangle, which means area of the triangle is Zero

The area of the triangle with vertices (x1, y₁); (x2, y2) and (x3, y3) is

X₁ (Y2−Ys)+X2(Ya—Y₁)+Xa(Y1 −Y2) |

Hence, substituting the points (x₁, y₁) = (k, 2k): (x2, y2) = (3k, 3k) and (x3, Y3) = (3,1) k(3k-1)+3k(1-2k)+3(2k-3k)

in the area formula, we get 2 (2k-3k) = 0

=> 3k²-k+ 3k - 6k2 + 6k9k = 0

=> -3k² - k = 0

-k (3k + 1) = 0

k = 0 ork = -⅓