Question #e1997

1 Answer
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:

#deltax = 6 - (-3)# and
#deltay = 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(deltax^2 + deltay^2) = sqrt(9^2 + (-1)^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.

#deltax/2 = 9/2 = 4.5#, so the x coordinate of the midpoint is -3 + 4.5 = 1.5

#deltay/2 = -1/2 = -0.5#, so the y coordinate is 4 + (-0.5) = 3.5