Question

Verify that the points (1, 5), (2, 3) and (-2, -1) are collinear or not.

Answer 1

Answer:

No the points are not collinear as per area of triangle formula

Step-by-step explanation:

the are of the triangle formed by the points is 10 but it should be zero

Answer 2

The points (1, 5), (2, 3) & (- 2, - 1) are not collinear.

Explanation:

The given points are (1, 5), (2, 3) and (- 2, - 1)

The equation of the line passing through the points (1, 5) and (2, 3) is

(y - 5)/(5 - 3) = (x - 1)/(1 - 2)

or, (y - 5)/2 = (x - 1)/(- 1)

or, y - 5 = - 2x + 2

or, 2x + y - 7 = 0 ..... (1)

Now we try to investigate if the point (- 2, - 1) satisfies the straight line (1)

Putting x = - 2 and y = - 1 in LHS of (1), we get

2 (- 2) + (- 1) - 7 = - 4 - 1 - 7 = - 12 ≠ 0, not satisfying the equation

Thus (- 2, - 1) does not lie on (1)

∴ the points (1, 5), (2, 3) & (- 2, - 1) are not collinear.