Answer:
[tex]S = (2,5)[/tex]
Step-by-step explanation:
Given
[tex]T = (0,3)[/tex]
[tex]Midpoint (M) =(1,4)[/tex]
Required
Determine the other end point (S)
Midpoint is calculated as thus:
[tex]M(x,y) = (\frac{S_x + T_x}{2},\frac{S_y + T_y}{2})[/tex]
This gives:
[tex](1,4) = (\frac{S_x + 0}{2},\frac{S_y + 3}{2})[/tex]
[tex](1,4) = (\frac{S_x}{2},\frac{S_y + 3}{2})[/tex]
Multiply through by 2
[tex]2 * (1,4) = (\frac{S_x}{2},\frac{S_y + 3}{2}) * 2[/tex]
[tex](2,8) = (S_x,S_y + 3)[/tex]
By comparison:
[tex]S_x = 2[/tex]
[tex]S_y + 3 = 8[/tex]
[tex]S_y = 8 - 3[/tex]
[tex]S_y = 5[/tex]
Hence:
The coordinates of S is
[tex]S = (2,5)[/tex]
