Segment Division using Section Formula

00:00 12 marks

Given two points A(2, 3) and B(8, 15) in a Cartesian plane, determine the coordinates of point P that divides the line segment AB in the ratio 2:3 internally and externally.

(a) For internal division, point P lies between A and B.

(b) For external division, point P lies outside the segment AB.

Part a

5 minutes 5 marks

Question

Calculate the coordinates of point P that divides the line segment AB internally in the ratio 2:3.

Hint Hint

Hint

Use the formula: For internal division, \(P = \left(\frac{n x_A + m x_B}{m+n}, \frac{n y_A + m y_B}{m+n}\right)\), where the ratio AP:PB = m:n. Here, m = 2 and n = 3.

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Complete Answer

P = (\(\frac{22}{5}\), \(\frac{39}{5}\)) = (4.4, 7.8)

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Part b

7 minutes 7 marks

Question

Calculate the coordinates of point P that divides the line segment AB externally in the ratio 2:3.

Hint Hint

Hint

For external division, use the formula: \(P = \left(\frac{m\,x_B – n\,x_A}{m-n}, \frac{m\,y_B – n\,y_A}{m-n}\right)\). Here, take m = 2 and n = 3.

Answer Answer
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Complete Answer

P = (-10, -21)

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