These three points are collinear. (3, 6), (-2, -9), (0, -4). True or False

Solution:

The three points are collinear or not can be determined by proving that they lie on the same straight line.

And that can be determined by verifying whether the line joining the three points have the same slope or not.

If there are points (x₁, y₁) and (x₂, y₂) joined by a straight line then the slope of the line will be given by:

Slope = (y₂ - y₁)/(x₂ - x₁) --- (1)

A) Lets find out the slope of the line joining points A (3, 6) and B(-2, -9)

As per equation (1) the slope will be:

Slope of Line AB = (-9 - 6)/(-2 - 3)

= -15/-5

= 3

B) Lets find out the slope of the line joining points B(-2, -9) and C(0, -4)

Slope of line BC = (-4 - (-9))/(0 - (-2))

=( -4 + 9)/2

= 5/2

C) Lets find out the slope of the line joining points A(3, 6) and C(0, -4)

Slope of line AC = (-4 - 6)/(0 - 3)

= -10/-3

= 10/3

Since the slopes of line AB ≠ Slope of Line BC ≠ Slope of Line AC these lines are not collinear.

These three points are collinear. (3, 6), (-2, -9), (0, -4). True or False

Summary:

These three points are collinear. (3, 6), (-2, -9), (0, -4) is a false statement.