Question

I need to find the distance between points d (A, B) and the middle of the segment AB(with line segment)

A(- 1/4 1),B(5/2, 3/4)

Answer 1

This is how I've interpreted your question.

Consider AB as the hypotenuse of a right triangle, with the vertical leg length equal to the difference between the y coords of A and B: 1-¾=¼, and horizontal leg length equal to the difference between x coords of A and B: 5/2+¼=11/4. From Pythagoras' Theorem: AB²=1/16+121/16=122/16. AB=√122/4. In other words, d(A,B)=√122/4 (approx 2.76).

The middle of AB is the average of coords: ((5/2-¼)/2,(1+¾)/2)=(9/8,7/8). The midpoint of AB is equidistant from A and B=√122/8 (approx 1.38).