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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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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)

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

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).

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