# What are the coordinates of the point (x, y) such that the distance between (x, y) and (4, 2) is half the distance between (x, y) and (8, 7)?

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In this problem we have to determine the point (x, y) that divides the line segment between (4, 2) and (8, 7) in the ratio 2:1

Now the coordinates of the point (x, y) that divides the distance between (x1, y1) and (x2, y2) in the ratio m : n is given by (n*x1 + m*x2)/(m + n), ((n*y1 + m*y2)/(m + n)

Substituting the values given here, the coordinates of the point are given by x = (2*4 + 8)/3 and y = (2*2 + 7)/3

=> x = 16/3 and y = 11/3

**The required point is (16/3, 11/3)**

If we assume (x,y) is a point onthe line joining (4,2) and (8,7) , then the the point (x,y) divides the line in the ratio 1:(1/2).

We know that a the point (x,y) that divides (x1,y1) and (x2,y2) in the ratio l:m are given by: (x,y) = ((mx1+lx2)/(l+m) , (my1+ly2)/(l+m)).

Therefore the coordinates of the point that divides line joining (4,2) and (8,7) in the ratio 1:1/2 or 2:1 is given by:

(x,y) = ((2*4+1*8)(1+2) , (2*2+1*7)/(1+2)) = (16/3 , 11/3).