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

Question

Abigail Allen · Accepted Answer

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

Hazel Anglin · Answer

undefined To find the distance between two points (x1, y1) and (x2, y2), you can use the distance formula:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

For the given points (4, -6) and (-2, 8), the distance is:

Distance = √((-2 - 4)^2 + (8 - (-6))^2)

To find the midpoint between two points (x1, y1) and (x2, y2), you can use the midpoint formula:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

For the given points (4, -6) and (-2, 8), the midpoint is:

Midpoint = ((4 + (-2))/2, (-6 + 8)/2)