# How do you find the coordinates of the other endpoint of a segment with the given A(-1,4) and midpoint M(3,-2)?

Mar 31, 2017

Coordinates of the other end point is $\left(7 , - 8\right)$

#### Explanation:

Look at the diagram also

Given -
A$\left(- 1 , 4\right)$
M$\left(3 , - 2\right)$

To find the mid point you have to use the formula

$\left(x , y\right) = \frac{{x}_{1} + {x}_{2}}{2} , \frac{{y}_{1} + {y}_{2}}{2}$

$x = 3$
$y = - 2$
${x}_{1} = - 1$
${y}_{1} = 4$

We have to find -

x_2=?
y_2=?

Plug in the values in the above formula

$\left(3 , 2\right) = \frac{- 1 + {x}_{2}}{2} , \frac{4 + {y}_{2}}{2}$

Then -

$\frac{- 1 + {x}_{2}}{2} = 3$
$- 1 + {x}_{2} = 3 \times 2 = 6$
${x}_{2} = 6 + 1 = 7$
${x}_{2} = 7$

$\frac{4 + {y}_{2}}{2} = - 2$
$4 + {y}_{2} = - 2 \times 2 = - 4$
${y}_{2} = - 4 - 4 = - 8$
${y}_{2} = - 8$

Coordinates of the other end point is $\left(7 , - 8\right)$