Exercise 12 Page 643

When we calculate a segments length in a coordinate plane we should consider the following:

• It's easier to find the lengths of horizontal and vertical segments.
• It's easier to find the length of a segment if one endpoint is at the origin.

  A square has four congruent sides, and four right angles. Therefore, the easiest way to place our square is with one vertice at the origin and have two of its sides run along the axes. At the same time, we will draw diagonals between opposite vertices.

  
  To find the length of the diagonal, we have to use the Distance Formula.
  d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)

  SubstitutePoints

  Substitute ( n,n) & ( 0,0)

  d = sqrt(( n - 0)^2 + ( n - 0)^2)

  SubTerms

  Subtract terms

  d = sqrt(n^2 + n^2)

  AddTerms

  Add terms

  d = sqrt(2n^2)

  CalcPow

  Calculate power

  d = nsqrt(2)
  The diagonal has a length of nsqrt(2).