Answer:
[tex](-6,9)[/tex]
Step-by-step explanation:
Midpoint: (0,3)
Endpoint: (6,-3)
Use the midpoint formula:
[tex]M=(\frac{x_{1}+x_{2}}{2} ,\frac{y_{1}+y_{2}}{2})[/tex]
Since you already have the midpoint and you need an endpoint, let the unknown endpoint be (x,y). Take the midpoint formula apart:
[tex]\frac{x_{1}+x{2}}{2}=m_{x}[/tex]
[tex]\frac{y_{1}+y_{2}}{2} =m_{y}[/tex]
[tex]m_{x}[/tex] and [tex]m_{y}[/tex] are the coordinates of the midpoint. Enter the known values of the midpoint into the equations:
[tex](0_{m_{x}},3_{m_{y}})\\\\\frac{x_{1}+x_{2}}{2}=0 \\\\\frac{y_{1}+y{2}}{2}=3[/tex]
Now enter the known endpoint values:
[tex](6_{x_{1}},-3_{y_{1}})\\\\\frac{6+x_{2}}{2}=0\\\\\frac{-3+y_{2}}{2}=3[/tex]
Solve for x. Multiply both sides by 2:
[tex]2*(\frac{6+x}{2})=2*(0)\\\\6+x=0[/tex]
Subtract 6 from both sides:
[tex]6-6+x=0-6\\x=-6[/tex]
Now solve for y. Multiply both sides by 2:
[tex]2*(\frac{-3+y}{2})=2*(3)\\\\ -3+y=6[/tex]
Add 3 to both sides:
[tex]-3+3+y=6+3\\y=9[/tex]
Now take the values of x and y and turn into a point:
[tex]x=-6\\y=9\\(-6,9)[/tex]
Finito.
