Question

prove that the points (a,b+c),(b,c+a),(c,a+b) are collinear and find the equation of straight line containing them​

Answer 1

Answer:

In all three of these points, the sum of the x- and y-coordinates is the same, namely a+b+c.  So all three points lie on the line with equation

 x + y = a + b + c.

Hope this helps!

Answer 2

Answer:

Step-by-step explanation:

Given, (a,b+c),(b,c+a),(c,a+b) ⇒  $\frac{y-y1}{y2-y1} = \frac{x-x1}{x2-x1\\}$

                                              ⇒  $\frac{y-b+c}{c+a-b+c} = \frac{x+a}{b-b}$

                                              ⇒  $\frac{y-b+c}{2c+a-b} = \frac{x+a}{0}$

                                              ⇒  y+x = a+b+c

Substituting C(c,a+b) in above equation.

              (a+b) + c = a+b+c

                  a+b+c = a+b+c

                          0 = 0

∴ Given points are collinear.

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