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Review: Section formula (dividing a segment in a ratio)

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Learn it A point dividing A to B in the ratio m : n is $P = \left(\frac{mx_2 + nx_1}{m + n}, \frac{my_2 + ny_1}{m + n}\right)$. It is $\frac{m}{m + n}$ of the way from A to B.

Example: Divide A(2, 1) to B(14, 9) in the ratio 1 : 3.

  1. x: $(1 \times 14 + 3 \times 2) \div 4 = 20 \div 4 = 5$.
  2. y: $(1 \times 9 + 3 \times 1) \div 4 = 12 \div 4 = 3$.
  3. P = (5, 3), one quarter of the way from A.

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