If the points (a,0), (0,b) and (1,1) are collinear then which of the following is true? 1a+1b=1 1a-1b=2 1a-1b=-1 1a+1b=2

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Deon Bowen · Accepted Answer

The area A of a triangle with vertices x1,y1,x2,y2 and x3,y3 calculate by the formula,  A        =            1    2                                1                                      x            1                                                y            1                                                1                                      x            2                                                y            2                                                1                                      x            3                                                y            3                                A        =            1    2                                1                          a                          0                                      1                          0                          b                                      1                          1                          1                    ⇒A=12a(b-1)+0(1-0)+1(0-b)⇒A=12ab-a-bThe area of the triangle with vertices a,0,0,b and (1,1) is zero as the given points (a,0), (0,b) and (1,1) are collinear.i.e.,                        A=0⇒12ab-a-b=0⇒ab-a-b=0⇒a+b=ab⇒a+bab=abab⇒1a+1b=1

If the points (a,0), (0,b) and (1,1) are collinear then which of the following is...

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