Find the midpoint and length of the line segment...?

Question

Find the midpoint and length of the line segment with the given endpoints:

(-5,8) and (9,-6)

Answer 1

The midpoint is exactly halfway between the two end-points, so just average the x and y coordinates.
x' = (-5 + 9) / 2
x' = 4 / 2
x' = 2

y' = (8 + -6) / 2
y' = 2 / 2
y' = 1

So the midpoint (x', y') is:
(2, 1)

As for the length of the line segment, just use the pythagorean theorem.
Figure the difference in the x coordinates... this is 9 minus -5.
= 9 - (-5)
= 9 + 5
= 14

Do the same for the y coordinates (8 minus -6)*:
= 8 - (-6)
= 8 + 6
= 14

(*I always put the bigger number first so that you get a positive length, but either way, remember to take the absolute value. Lengths should be positive.)

So this is a right triangle with two legs (a and b) that are both 14. You want the hypotenuse (c):
a² + b² = c²

14² + 14² = c²
196 + 196 = c²
c² = 392
c = √392
c = 14√2

Again there are two values for a square root (positive and negative), but you only care about the positive value for a length.
c = 14√2 units ≈ 19.8 units

Midpoint = (2, 1)
Length = 19.8 units

Answer 2

The midpoint formula is applied to your "x" values and "y" values. There let the midpint equal the average of x and the average of y. For x (9+(-5))/2 anf for y (-6+8))/2 the new point yields (2,1)

Answer 3

((9 - -5)^2 + (-6 - 8)^2) ^.5 = 19.7989 length
(9 + -5)/2, (-6 + 8)/2 = (2,1) midpoint

Answer 4

mid-x is: ( -5 + 9 ) / 2 = 2

mid-y is: ( 8 - 6 ) / 2 = 1

midpoint is (2,1)

length can be determined using the pythagorean theorem.

Aloha

Answer 5

midpoint = (2,1)
distance = sqrt[(14)^2+(14)^2]=19.79

Answer 6

mid point is (2,1)