what js the midpoint and the length of the segement with endpoints (4,6) and (-1,6)

Question

find the midpoint and the length of the segment with endpoints (4,6) and (-1,6)

Answer 1

Use the formulas for the length of a segment (the distance formula) and the midpoint formula:

 

The midpoint is at:

          ( (x₁+x₂)/2, (y₁+y₂)/2 )          [midpoint formula]

         ( ((4+(-1))/2, (6+6)/2 )

  The midpoint is (3/2, 6).

 

The length of the segment (use the distance formula):

  d =  √( (x₂-x₁)² + (y₂-y₁)² )             [distance formula]

  d =  √( ((-1)-4)² + (6-6)² )

  d =  √(25+0)

  d = 5

  The length is 5.

Answer 2

Use the distance formula and the coordinates of the two endpoints to find the length.

 

d = sqrt[(x₂ - x₁)² + (y₂ - y₁)²]

 

x₂ = -1         x₁ = 4

 

y₂ = 6          y₁ = 6

 

 

d = sqrt[(-1 - 4)² + (6 - 6)²]

 

   = sqrt(-5² + 0²)

 

   =  sqrt(25)

 

   = 5

 

So the length of the segment is 5.