Exercise 11 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 rectangle has two sets of opposite sides, and four right angles. Therefore, the easiest way to place our rectangle is with one vertex at the origin and to have it's width and length run along the axes. At the same time, we will draw diagonals between opposite vertices.

  
  To find the length of a diagonal, we have to use the Distance Formula. Note that it's always easier to work with points such as the origin so we will calculate the segment between (5,4) and (0,0).
  d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)

  SubstitutePoints

  Substitute ( 5,4) & ( 0,0)

  d = sqrt(( 5 - 0)^2 + ( 4 - 0)^2)

  SubTerms

  Subtract terms

  d = sqrt(5^2 + 4^2)

  CalcPow

  Calculate power

  d = sqrt(25 + 16)

  AddTerms

  Add terms

  d = sqrt(41)
  The diagonal has a length of sqrt(41).