How do you find the distance and midpoint between the two points. (4, -6) (-2, 8)?

1 Answer
Lovecraft
Oct 16, 2015

#d = 2sqrt(58)#
#M = (1,1)#

Explanation:

To find the distance we just apply Pythagoras. Think of it this way:

The difference between the #x# points causes a straight horizontal line, the difference between the #y# points causes a straight vertical line, so the distance between the two points is the hypotenuse, or

#d^2 = Deltax^2 + Deltay^2#

#d = sqrt(Deltax^2 + Deltay^2)#

#d = sqrt((-2-4)^2 + (8-(-6))^2)#

#d = sqrt(36 + 196)#

#d = sqrt(232)#

#d = sqrt(58*4) = 2sqrt(58)#

The midpoint between two points, #M#, is literally just the average between the #x# values and the average between the #y# values, or

#M = (bar x, bar y)#

We have that

#bar x = (4-2)/2 = 2/2 = 1#

And that

#bar y = (8 -6)/2 = 2/2 = 1#

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