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Question

For the line segment ST, S has coordinates S(3,8) and T is on the X-axis. The midpoint M, of ST is on the Y-axis. Find the coordinates of T and M. Provide necessary let statements and conclusion. An algebraic solution is expected.

Answer 1

Points on the x-axis contain the point (x, 0).

Points on the y-axis contain the point (0, y)

 

The midpoint formula is

 

M_ST = ( (S_x + T_X) / 2 , (S_y + T_y) / 2 )

 

 

So to the find the coordinate of M and T,

 

(0, y) = ( (3 + T_x) / 2 , (8 + 0) / 2 )

 

 

Given this, we can write a system of equations.

 

(3 + T_x) / 2 = 0                and            (8 + 0) / 2 = y

 

 

Solve for T_x from the first equation and solve for y from the second equation.

Answer 2

Mid point is given by ((3+x)/2, 4)

since it is on the y axis means that (3+x)/2 have to be 0

so 3+x=0 means x=-3

therefore the mid points coordinates (0, 4)

and the T coordinates (-3,0)