What is the point B which lies on the line AC and is 5 units away from A (3, 7) and 2 units away from C (1, 2)?  

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We need to find the point B which lies on AC and which is 5 units away from (3, 7) and 2 units away from (1, 2).

We use the relation that the coordinates of a point on a line between A(x1, y1) and B(x2, y2) and the distance of which from A and B is in the ratio m:n resp. is given by (n*x1 + m*x2)/(m+n) , (n*y1 + m*y2)/(m+n)

The ratio of the distance of the point B from A and C is 5:2. 5+2 is equal to 7.

The coordinates of this point B are given by [(5*1 + 2*3)/7, (5*2 + 2*7)/7]

=> [11 / 7, 24/7].

The required point is (11/7, 24/7)

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