Question

Given the midpoint and one of the endpoints of a line segment, find the other endpoint. Midpoint: (0,3) Endpoint: (6,-3)

Answer 1

Answer:

$(-6,9)$

Step-by-step explanation:

Midpoint: (0,3)

Endpoint: (6,-3)

Use the midpoint formula:

$M=(\frac{x_{1}+x_{2}}{2} ,\frac{y_{1}+y_{2}}{2})$

Since you already have the midpoint and you need an endpoint, let the unknown endpoint be (x,y). Take the midpoint formula apart:

$\frac{x_{1}+x{2}}{2}=m_{x}$

$\frac{y_{1}+y_{2}}{2} =m_{y}$

$m_{x}$ and $m_{y}$ are the coordinates of the midpoint. Enter the known values of the midpoint into the equations:

$(0_{m_{x}},3_{m_{y}})\\\\\frac{x_{1}+x_{2}}{2}=0 \\\\\frac{y_{1}+y{2}}{2}=3$

Now enter the known endpoint values:

$(6_{x_{1}},-3_{y_{1}})\\\\\frac{6+x_{2}}{2}=0\\\\\frac{-3+y_{2}}{2}=3$

Solve for x. Multiply both sides by 2:

$2*(\frac{6+x}{2})=2*(0)\\\\6+x=0$

Subtract 6 from both sides:

$6-6+x=0-6\\x=-6$

Now solve for y. Multiply both sides by 2:

$2*(\frac{-3+y}{2})=2*(3)\\\\ -3+y=6$

Add 3 to both sides:

$-3+3+y=6+3\\y=9$

Now take the values of x and y and turn into a point:

$x=-6\\y=9\\(-6,9)$

Finito.