Question

Show that (1,3),(-2,-6),(2,6) are collinear and find the equation of the line L containing them

Answer 1

Answer:

1. area of triangle is equal to 0.

2. for find equation

find slope and put in the equation

y-3=m(x-1) m is slope

Answer 2

Given,

We are given three coordinates of a line  (1,3) , (-2,-6) , (2,6).

To find,

First, we have to prove that the three points are collinear and then we also have to find the equation of Line L containing them.

Solution,

1. A-line with three given coordinates can be proved collinear by two methods: Find the area of a triangle with three given coordinates, if the area comes out to be zero, then the line must be collinear.
2. If L is a collinear line with points A, B, and C lying on it. Then the slope of AB =  the slope of BC = the slope of CA.

Now,

A(1,3) , B(-2,-6) , C(2,6)

Slope of AB = (-6-3)/(-2-1) = (-9)/(-3) = 3.

Slope of BC = (6-(-6))/(2-(-2)) = (12)/(4) = 3.

Slope of CA = (3-6)/(1-2) = (-3)/(-1) = 3.

Since, Slope of AB = Slope of BC = Slope of CA.

Hence, proved  (1,3) , (-2,-6) , (2,6) are collinear.

Equation of line L containing them is:

⇒ (y - 3)/(x - 1) = 3

⇒ y - 3 = 3x -3

⇒ 3x - y = 0.

Hence, the three points are collinear and the equation of the line L containing them is 3x - y = 0.