Show that the points A (a, b+c), B (b, c + a) and C (c, a + b) are collinear.

### Asked by Topperlearning User | 24th Nov, 2013, 05:23: AM

Expert Answer:

### If the given points are collinear then the area of the triangle formed by joining these points is zero.
_{}
Here, x_{1} = a, y_{1} = b + c; x_{2} = b, y_{2} = c + a; x_{3} = c, y_{3} = a + b.
Substituting the values in the formula for area of a triangle, you get
_{}_{}
_{}_{}
_{}ac - ab + ab - bc + bc - ac = 0
Hence the given points are collinear.

_{}

_{1}= a, y

_{1}= b + c; x

_{2}= b, y

_{2}= c + a; x

_{3}= c, y

_{3}= a + b.

_{}

_{}

_{}

_{}

_{}ac - ab + ab - bc + bc - ac = 0

### Answered by | 24th Nov, 2013, 07:23: AM

## Application Videos

## Concept Videos

- question
- in each of the following find the value of k for which the points are collinear . 1) (7,-2), (5,1) ,(3,k)
- In each of the following, find the value of a for which the given points are collinear. (ii) (a-3-2a), (-a+1,2a) and (-4-a,6-2a)
- The 27th question...
- Find the area of the Triangle ABC, with vertex A(1,-4) and midpoint of AB and AC as X(2,-1) and Y(0,-4) respectively.
- in RD Sharma's solution , ex.6.5 , Q.24, why we have taken the value 1/2 with both positive and negative sign. What is the reason for doing this?????
- find the area of triangle whose vertices are( - 8, 4)( - 6, 6) and (-3, 9)
- If (2,4),(2t,6t),(3,8) are collinear, then t=
- Find the area of a triangle whose vertices are A(6,3), B(-3,5) and C(4,-2).

### Kindly Sign up for a personalised experience

- Ask Study Doubts
- Sample Papers
- Past Year Papers
- Textbook Solutions

#### Sign Up

#### Verify mobile number

Enter the OTP sent to your number

Change