Question

What are the coordinates of point S"? (negative three-halves, nine-halves) (negative nine-halves, fifteen-halves) (nine-halves, negative three-halves) (negative fifteen-halves, 0)

Answer 1

`S=((9)/(2),-(3)/(2))`

Explanation:

The missing details are:

`T= (0,4)`

`M = ((9)/(4), (5)/(4))` --- Midpoint of ST

Required

Determine the coordinates of S

To do this, we apply the mid-point formula:

`M(x,y) = (1)/(2)(x_1+x_2,y_1+y_2)`

Where

`M(x,y) = ((9)/(4), (5)/(4))`

`T(x_1,y_1) - (0,4)`

The equation becomes:

`M(x,y) = (1)/(2)(x_1+x_2,y_1+y_2)`

`((9)/(4),(5)/(4)) = (1)/(2)(0+x_2,4+y_2)`

`((9)/(4),(5)/(4)) = (1)/(2)(x_2,4+y_2)`

Multiply through by 2

`2*((9)/(4),(5)/(4)) = 2*(1)/(2)(x_2,4+y_2)`

`((9)/(2),(5)/(2)) = (x_2,4+y_2)`

By comparison:

`x_2 = (9)/(2)`

`4 + y_2 =(5)/(2)`

`y_2 =(5)/(2)-4`

`y_2 =(5-8)/(2)`

`y_2 =-(3)/(2)`

Hence, the coordinates of S is:

`S=((9)/(2),-(3)/(2))`