#### Question

Given A(4, –3), B(8, 5). Find the coordinates of the point that divides segment AB in the ratio 3 : 1.

#### Solution

Let the coordinate of the point which divide the line AB in the ratio 3 : 1 be P(a, b)

\[a = \frac{3 \times 8 + 1 \times 4}{3 + 1} = \frac{24 + 4}{4} = 7\]

\[b = \frac{3 \times 5 + 1 \times \left( - 3 \right)}{3 + 1} = \frac{15 - 3}{4} = 3\]

P(a, b) = (7, 3)

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Solution Given A(4, –3), B(8, 5). Find the Coordinates of the Point that Divides Segment Ab in the Ratio 3 : 1. Concept: Division of a Line Segment.