Midpoint Line question?

Question

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. 

 

OK so, I know what S that (6,2), and that since t is on the y-axis, it is equal to (0,y), and so the midpoint is (x,0). But from there, I'm not sure how to use the midpoint formula to figure out the x and y values. 

 

M_{ST =(}x₁+x₂/2, y₁+y₂/2)

(x,0)=(6+0/2 , 2+y/2)

 

Thank you for helping! I have a quiz tomorrow so I'm just reviewing questions and got stuck on this one... 

Answer 1

The midpoint M is on the x-axis.  So the coordinate of M is (x, 0), just as you indicated.  T is on the y-axis, making the coordinate of T (0, y).  So far, so good.

 

S and T are the endpoints.

 

Point S = (6, 2)

Point T = (0, y)

M = (x, 0)

 

Using the formula for midpoint that you have here,

 

(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)