Question

using the concept of slop show that the points (-2,5),(6,-1) and (2,2) are coilinear

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that the points (-2,5),(6,-1) and (2,2) are represented as

Coordinates of A be (- 2, 5)

Coordinates of B be (6, - 1)

Coordinates of C be (2, 2)

Now, in order to show that three points A, B, C are collinear, we have to show that Slope of AB = Slope of BC.

And

Slope of line segment joining the points A (a, b) and B (c, d) is evaluated as

$\rm :\longmapsto\:\boxed{\tt{ \: \: Slope \: = \: \frac{d - b}{c - a} \: \: }}$

So,

Slope of AB joining the points A (- 2, 5) and B(6, - 1) is

$\rm :\longmapsto\:Slope \: of \: AB = \dfrac{ - 1 - 5}{6 - ( - 2)} = \dfrac{ - 6}{8} = - \dfrac{3}{4}$

Now,

Slope of BC joining the points B(6, - 1) and C(2, 2) is

$\rm :\longmapsto\:Slope \: of \: BC \: = \: \dfrac{2 - (1)}{2 - 6} = \dfrac{3}{ - 4} = - \dfrac{3}{4}$

So, from above we concluded that

$\rm :\longmapsto\:Slope \: of \: AB = Slope \: of \: BC$

$\sf\implies \: AB \: \parallel \: BC$

$\rm\implies \: A, \: B, \: C \: are \: collinear$

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EXPLORE MORE

1. Slope of a line is defined as the tangent of the angle which a line makes with positive direction of x axis measured in anti-clockwise direction and is denoted by the symbol m and is given by m = tanp where p is the angle.

2. Two lines having slope m and M are parallel iff m = M

3. Two lines having slope m and M are perpendicular iff Mm = - 1

4. If a line is parallel to x- axis or it self x - axis, its slope is 0.

5. If a line is parallel to y- axis or it self y - axis, its slope is undefined.