Question

Question #e1997

Answer 1

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