For the line segment ST, S has coordinates (6,2) and T is on the y-axis. The midpoint of ST is on the x-axis. Find the coordinates of T and M.

Question

M stands for midpoint 

Answer 1

The midpoint M is on the x-axis.  So the coordinate of M is (x, 0).  T is on the y-axis, making its coordinate (0, y). 
 
S and T are the endpoints.
 
Point S = (6, 2)
Point T = (0, y)
M = (x, 0)
 

The formula for midpoint is

 

M = ((x₁ + x₂) / 2  ,   (y₁ + y₂) / 2)

 

 

Plug in the given the values into this formula.
 
(x, 0) = ((6 + 0) / 2  ,    (2 + y) / 2))
 
(x, 0) = ((6 / 2) ,  (2 + y) / 2)
 
 
Next we write two equations.  One for x coordinate and the other for y-coordinate.
 
x = 3                and               0 = (2 + y) / 2
                                            0 = 2 + y
                                            -2 = y
 
 
Plugging in these values into the coordinate points,
 
M = (3, 0)
T = (0, -2)