Answer:
[tex]S=(\frac{9}{2},-\frac{3}{2})[/tex]
Step-by-step explanation:
The missing details are:
[tex]T= (0,4)[/tex]
[tex]M = (\frac{9}{4}, \frac{5}{4})[/tex] --- Midpoint of ST
Required
Determine the coordinates of S
To do this, we apply the mid-point formula:
[tex]M(x,y) = \frac{1}{2}(x_1+x_2,y_1+y_2)[/tex]
Where
[tex]M(x,y) = (\frac{9}{4}, \frac{5}{4})[/tex]
[tex]T(x_1,y_1) - (0,4)[/tex]
The equation becomes:
[tex]M(x,y) = \frac{1}{2}(x_1+x_2,y_1+y_2)[/tex]
[tex](\frac{9}{4},\frac{5}{4}) = \frac{1}{2}(0+x_2,4+y_2)[/tex]
[tex](\frac{9}{4},\frac{5}{4}) = \frac{1}{2}(x_2,4+y_2)[/tex]
Multiply through by 2
[tex]2*(\frac{9}{4},\frac{5}{4}) = 2*\frac{1}{2}(x_2,4+y_2)[/tex]
[tex](\frac{9}{2},\frac{5}{2}) = (x_2,4+y_2)[/tex]
By comparison:
[tex]x_2 = \frac{9}{2}[/tex]
[tex]4 + y_2 =\frac{5}{2}[/tex]
[tex]y_2 =\frac{5}{2}-4[/tex]
[tex]y_2 =\frac{5-8}{2}[/tex]
[tex]y_2 =-\frac{3}{2}[/tex]
Hence, the coordinates of S is:
[tex]S=(\frac{9}{2},-\frac{3}{2})[/tex]
