Question

How do I show that (1,-1), (-1,5) and (3,-7) are collinear?

Answer 1

Given :

• The points (1 , -1) , (-1 , 5) and (3 , -7) .

To Show :

• The given points are collinear.

Formula to be used :

The gradient of the points (x₁ , y₁) and (x₂ , y₂) is given by :

• $\longrightarrow\sf{\dfrac {y_{2} - y_{1}}{x_{2} - x_{1}}}$

Solution :

Let us consider A (1 , -1) , B (-1 , 5) and C(3 , -7)

If Gradient of AB = Gradient of BC then the points A , B and C are collinear

Now gradient of AB :-

$=\sf{\dfrac{5 - (-1)}{-1-1}}\\\\ =\sf{\dfrac{6}{-2}}\\\\ =\sf{-3}$

And the gradient of BC :

$\sf{=\dfrac{-7-5}{3-(-1)}}\\\\ = \sf{\dfrac{-12}{4}}\\\\ = \sf{-3}$

Thus,

Gradient of AB = Gradient of B.C.

Hence A(1 , -1) , B(-1 , 5) , C(3 , -7) are Collinear.

Answer 2

Step-by-step explanation:

Let us consider A (1 , -1) , B (-1 , 5) and C(3 , -7)

If Gradient of AB = Gradient of BC then the points A , B and C are collinear

Now gradient of AB :-

5 - ( - 1 )/( - 1 - 1)

= 6/-2

= -3

And the gradient of BC :

(-7 - 5)/ ( 3 - (- 1) )

= -12/ 4

= -3

Since,

Gradient of AB = Gradient of B.C.

Hence A(1 , -1) , B(-1 , 5) , C(3 , -7) are Collinear.