The distance between points (a + b, b + c) and (a – b, c – b) is ____ units. A ) 2 a 2 + b 2 B ) 2 b 2 + c 2 C ) 2 2 b D ) 2 a 2 − c 2

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The distance between points (a + b, b + c) and (a – b, c – b) is ____ units.    A  )  2            a      2        +          b      2          B  )  2            b      2        +          c      2          C  )  2      2    b    D  )  2            a      2        −          c      2

tabuaa5q · Accepted Answer

The true option is  B   2      2    bThe separation of two points   (      x    1    ,      y    1    ) and   (      x    2    ,      y    2    )  =      (          x      2        −          x      1              )      2        +    (          y      2        −          y      1              )      2       Let&#039;s name the points as A(a + b, b + c) and B(a - b, c - b) .   A  B  =      (          x      2        −          x      1              )      2        +    (          y      2        −          y      1              )      2          ⇒  A      B    2    =  (  a  +  b  −  (  a  −  b  )      )    2    +  (  b  +  c  −  (  c  −  b  )      )    2      ⇒  A      B    2    =  4      b    2    +  4      b    2    =  8      b    2      ⇒  A  B  =  2      2    b  Consequently, the space between points (a + b, b + c) and (a – b, c – b) is   2      2    b units.

The distance between points (a + b, b + c) and (a – b, c – b) is ____ units. 2 sqrt(a^2+b^2), 2 sqrt(b^2+c^2), 2 sqrt(2)b, 2 sqrt(a^2-c^2)

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