Find the distance between A(2,5) and B(a,b) . The point m(-1,3) is the midpoint of AB.

The answer posted above gives the coordinates of the point B,
whereas the answer required is the distance between the points A and
B.

To find this distance it is not necessary to find the coordinates
of B. Since coordinates of A and mid point m of AB are given, we can simply find the distance Am,
and double it to get the distance
AB.

Solution:

Distance between any two
points (x1, y1) and (x2, y20 is given by:

Distance = [(x2 - x1)^2 +
(y2 - y)^2]^(1/2)

Therefore:

Distance
Am = [(-1 - 2)^2 + (3 - 5)^2]^(1/2)

= (9 + 4)^(1/2) =
13^(1/2)

Distance AB = 2*Distance Am = 2*13^(1/2) =
7.2111