# If a segment has an endpoint at (3, 2) and the midpoint at (-1, 2), what are the coordinates of the other endpoint?

Apr 22, 2018

$\left(- 5 , 2\right)$

#### Explanation:

The distance from the midpoint to the first endpoint is $4$, which means that the other endpoint will be at the exact same distance from the midpoint as the first endpoint. So, four to the left of $\left(- 1 , 2\right)$ is $\left(- 5 , 2\right)$

Apr 23, 2018

Coordinates of other endpoint$= - 5 , 2$

#### Explanation:

Let the first endpoint be $A$ and midpoint be $B$ and other endpoint be $C$

Distance A to B:-

$\therefore = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$

$\therefore = \sqrt{{\left(\left(- 1\right) - \left(3\right)\right)}^{2} + {\left(2 - 2\right)}^{2}}$

:.=sqrt((-4)^2+0

$\therefore = \sqrt{16}$

$\therefore = A \to B =$4units

The segment is a vertical line because the$y$ values of
$A \mathmr{and} B = 2$

Coords of $B = - 1 , 2$

The bearing of the line $B \to C$$= {180}^{\circ}$

$\therefore \cos {180}^{\circ} = - 1 \times 4.0 = - 4$ add to$x$ coord of $B$ then

$\therefore C$=-5$= x$ coord.

$\therefore \sin {180}^{\circ} = 0 \times 4.0 = 0$ add to$y$ coord of $B$ then

$\therefore C$=2$= y$ coord.

Coordinates of $C = - 5 , 2$

Apr 23, 2018

color(blue)((-5,2)#

#### Explanation:

The coordinates of the midpoint of a line is given by:

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

Let the coordinates of the unknown end be:

$\left({x}_{2} , {y}_{2}\right)$

We know the coordinates of the midpoint are:

$\left(- 1 , 2\right)$

So:

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

And:

$\frac{3 + {x}_{2}}{2} = - 1 \implies {x}_{2} = - 5$

$\frac{2 + {y}_{2}}{2} = 2 \implies {y}_{2} = 2$

Coordinates:

$\left(- 5 , 2\right)$