Question

Can someone do this question without using area of triangle formula​

Answer 1

Yes I can do this without using area of triangle formula

I will use the concept of slopes to find k .

We know that

• If three points are collinear then slopes of point is always equal.

Here We have

• A = (k + 1 , 2k)
• B = (3k , 2k + 3)
• C = (5k - 1 , 5k)

Slope of the line joining two points (x₁ , y₁) and (x₂, y₂)

= (y₂ - y₁) / (x₂ - x₁)

Slope of AB = [2k - (2k + 3)] / [3k - (k + 1)]

= [2k - 2k - 3] / [3k - k - 1]

= -3 / 2k - 1

Slope of BC = [5k - (2k + 3)] / [(5k - 1) - 3k]

= [5k - 2k - 3] / [5k - 1 - 3k]

= [3k - 3] / [2k - 1]

Slope of AB = Slope of BC

-3 / 2k - 1 = (3k - 3) / (2k - 1)

-3 = 3k - 3

0 = 3k

k = 0