# Question #e1997

Sep 21, 2017

length: 9.055

midpoint coordinates: (1.5, 3.5)

#### Explanation:

Segment AB forms the hypotenuse of a right triangle with legs equal to:

$\delta x = 6 - \left(- 3\right)$ and
$\delta y = 3 - 4$

(you can plot the two points on graph paper and confirm this)

So, the length of the legs are 9 and -1. Fall back on your old pal Pythagoras to find the length:

$l = \sqrt{\delta {x}^{2} + \delta {y}^{2}} = \sqrt{{9}^{2} + {\left(- 1\right)}^{2}}$

$= \sqrt{82} = 9.055$

To find the midpoint, simply divide the length of the legs and add that to coordinates of the leftmost point.

$\delta \frac{x}{2} = \frac{9}{2} = 4.5$, so the x coordinate of the midpoint is -3 + 4.5 = 1.5

$\delta \frac{y}{2} = - \frac{1}{2} = - 0.5$, so the y coordinate is 4 + (-0.5) = 3.5