find the distance between each of points and find the midpoint

Question

these are the given points. (2/3, 3/2), (-2, -4)

Answer 1

Given points say (x1,y1) = (2/3, 3/2)

(x2,y2) = (-2, -4)

Distance between the points = √[(-2-2/3)^2+(-4-3/2)^2]

=√[(-8/3)^2+(-11/2)^2]

= √(64/9+121/4)

= √((64*4+121*9)/36)

= √(256+1089/36)

= √(1345/36)

= √(1345)/6

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

= [(2/3-2)/2, (3/2-4)/2]

=(-4/6, -5/4)

= (-2/3,-5/4)

Midpoint of given two points is (-2/3,-5/4) and distance is √(1345)/6.