Find the distance between A(2,5) and B(a,b) . The point m(-1,3) is the midpoint of AB.
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Given the points:
A(2,5) B(a,b) and m(-1,3) is midpoint of AB
We need to determine the point B(a,b)
Then we will use the midpoint formula to solve for B:
We know that:
mx = ( Ax+Bx)/2
==> -1 = ( 2 + a)/2
==> -2 = 2 + a
==> a = -4
Also :
my = (yA+yB)/2
==> 3 = (5+b)/2
==? 6 = 5+ b
==> b= 1
Then the point B is: B(-4,1)
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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
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