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CLASS 10 MATHS · COORDINATE GEOMETRY

Section formula

The point dividing A(x₁, y₁) and B(x₂, y₂) internally in the ratio m : n is ((mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n)).

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Worked examples

Example 1 · level 1

Find the point that divides the segment joining A(3, −3) and B(15, −11) internally in the ratio 1 : 3.

  1. (6, −9)
  2. (12, −9)
  3. (6, −5)
  4. (−5, 6)
Show solution
  1. x = (1 × 15 + 3 × 3) ÷ 4 = 24 ÷ 4 = 6.
  2. y = (1 × (−11) + 3 × (−3)) ÷ 4 = −20 ÷ 4 = −5.
  3. Point = (6, −5).

Answer: (6, −5)

Example 2 · level 2

Find the point that divides the segment joining A(6, 1) and B(−9, 11) internally in the ratio 3 : 2.

  1. (−3, 7)
  2. (0, 5)
  3. (−3, 5)
  4. (7, −3)
Show solution
  1. x = (3 × (−9) + 2 × 6) ÷ 5 = −15 ÷ 5 = −3.
  2. y = (3 × 11 + 2 × 1) ÷ 5 = 35 ÷ 5 = 7.
  3. Point = (−3, 7).

Answer: (−3, 7)

Example 3 · level 3

In what ratio does the point (5, 5) divide the line segment joining A(−1, 2) and B(7, 6)? (write like 2:3)

Show solution
  1. AP : PB along x = (5 − (−1)) : (7 − 5) = 6 : 2.
  2. Simplify: 3 : 1. (The y-coordinates give the same ratio.)

Answer: 3:1

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