Question

The graph of line segment AB is shown below. 
a) Use the graph to find the coordinates of points A and B. 
b) Find the length of the line segment AB. 
c) Find the midpoint of the line segment AB.

Answer 1

a)

Observe the graph 

The points are A = (-2, 4) and B  = (4, 2).

The point 

b)

Let A (x1, y1) = (-2, 4) and B (x2, y2) = (4, 2)

Lenth of the Line Segment =    √ [(x2 - x1)^2 + (y2 - y1)^2]

Substitute  (x1, y1) = (-2, 4) and  (x2, y2) = (4, 2) in above equation

AB  =  √ [(4 + 2)^2 + (2 - 4)^2]

      =  √ [(6)^2 + (-2)^2]

      =  √ (36 + 4)

      =  √ (40)

      =  2√ 10

c)

Midpoint of the line AB (M) =   ( (x1 + x1)/2 , (y1 + y2)/2 )

Substitute  (x1, y1) = (-2, 4) and  (x2, y2) = (4, 2) in above equation

M  =   ( (-2 + 4)/2 , (4 + 2)/2 )

     =   ( 2/2 , 6/2 ) 

     =   ( 1 , 3 ) 

Answer : 

a)  The points are A = (-2, 4) and B  = (4, 2).

b)  Lenth of the Line Segment AB =  2√ 10.

c)  Midpoint of the line AB = (1, 3).