Exercise 9 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.

  Therefore, to make things easy for us we will place the right angle vertiex at the origin, have one leg run along the vertical axis and another side run along the horizontal axis.

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

  SubstitutePoints

  Substitute ( 9,0) & ( 0,7)

  d = sqrt(( 9 - 0)^2 + ( 0 - 7)^2)

  SubTerms

  Subtract terms

  d = sqrt(9^2+(- 7)^2)

  CalcPow

  Calculate power

  d = sqrt(81+49)

  AddTerms

  Add terms

  d = sqrt(130)
  The hypotenuse has a length of sqrt(130) units.