Question

Which of the following is or are correct statements for conditions of col-linearity of three points

$A(x_1,y_1),B(x_2,y_2)andC(x_3,y_3)?$
1.slope of line AB = slope of line BC = slope of line CA
2.Area of $△$ABC = 0
3. AC = AB + BC or AB ˜BC

• A. only 1
• B. only 1 and 2
• C. only 2 and 3
• D. all 1, 2 and 3

Answer 1

The correct option is D

all 1, 2 and 3

If points A,B are collinear

Then

If points A,B and C are collinear

AB and BC will be the part of line segment AC

Then, slope of line AB = slope of line BC = slope of line AC

2. If these points are collinear

There won't be formation of triangle

So, Area of triangle ABC = 0

3. If point B is the somewhere in the line segment AC then

AC = AB + BC

In general we can say

AC = ( AB˜ BC)

Point can externally divided the line segment AB

AC = AB - BC or BC - AB

So, all the given three statements are correct.