NumericalModerate3 marks
P(1, -2) is a point on the line segment A(3, -6) and B(x, y) such that, AP : PB is equal to 2 : 3. Find the coordinates of B.
Topic: Section / midpoint / centroid
Previous-year question practice database
Answer
Exam answer
A(3,−6), B(x,y), P(1,−2). AP:PB = 2:3.
Section formula: P = ((2x + 3×3)/5, (2y + 3×(−6))/5).
For x: 1 = (2x+9)/5 5 = 2x+9 x = −2.
For y: −2 = (2y−18)/5 −10 = 2y−18 y = 4.
Answer: B = (−2,4).
Explanation
Apply the internal section formula for ratio AP:PB = 2:3.
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