Help with some algebraCan anybody explain to me how they went from this y − y 1 = y 2 − y 1 x 2 − x 1 ( x − x 1 )to this. ( y 1 − y 2 ) · x − ( x 1 − x 2 ) · y − ( y 1 − y 2 ) · x 1 + ( x 1 − x 2 ) · y 1 = 0Its confusing..

Question

Help with some algebraCan anybody explain to me how they went from this  y  −      y    1    =                    y        2            −              y        1                            x        2            −              x        1              (  x  −      x    1    )to this.  (      y    1    −      y    2    )  ·  x  −  (      x    1    −      x    2    )  ·  y  −  (      y    1    −      y    2    )  ·      x    1    +  (      x    1    −      x    2    )  ·      y    1    =  0Its confusing..

crociandomh · Accepted Answer

Ok! So you just got to multiply by   (      x    2    −      x    1    ) on both sides to obtain  (  y  −      y    1    )  (      x    2    −      x    1    )  =  (      y    2    −      y    1    )  (  x  −      x    1    )Now you can expand by multiplying each bracket to obtain:  y  (      x    2    −      x    1    )  −      y    1    (      x    2    −      x    1    )  =  x  (      y    2    −      y    1    )  −      x    1    (      y    2    −      y    1    )Where in the right hand side, I multiplied each term of the second bracket by the whole first bracket. Now observe that   (      x    2    −      x    1    )  =  −  (      x    1    −      x    2    ) and the same with   (      y    2    −      y    1    )  =  −  (      y    1    −      y    2    ), you can see this since  −  (      x    1    −      x    2    )  =  −      x    1    +      x    2    =      x    2    −      x    1  Can you finish it?

Help with some algebra Can anybody explain to me how they went from this y −

Answered question

Answer & Explanation

New Questions in Pre-Algebra