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Line segment AB joining the points A = (0, -10) and B = (20, 5) is divided internally into five equal parts by points P, Q, R and S. The co-ordinates of points Q are :

  1. (8, -4)

  2. (4, -8)

  3. (-8, -4)

  4. (-4, -8)

Section Formula

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Answer

By section formula,

(x, y) = (m1x2+m2x1m1+m2,m1y2+m2y1m1+m2)\Big(\dfrac{m1x2 + m2x1}{m1 + m2}, \dfrac{m1y2 + m2y1}{m1 + m2}\Big)

From figure,

Line segment AB joining the points A = (0, -10) and B = (20, 5) is divided internally into five equal parts by points P, Q, R and S. The co-ordinates of points Q are : 1. (8, -4) 2. (4, -8) 3. (-8, -4) 4. (-4, -8). Model Paper 5, Concise Mathematics Solutions ICSE Class 10.

Q divides line segment AB in the ratio 2 : 3.

∴Q=(2×20+3×02+3,2×5+3×−102+3)=(40+05,10−305)=(405,−205)=(8,−4).\therefore Q = \Big(\dfrac{2 \times 20 + 3 \times 0}{2 + 3}, \dfrac{2 \times 5 + 3 \times -10}{2 + 3}\Big) \\[1em] = \Big(\dfrac{40 + 0}{5}, \dfrac{10 - 30}{5}\Big) \\[1em] = \Big(\dfrac{40}{5}, \dfrac{-20}{5}\Big) \\[1em] = (8, -4).

Hence, Option 1 is the correct option.

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