Finding the ratio of division sheet3-mark answer frameFind the ratio in which the x-axis divides the segment joining A(−1, −6) and B(5, 3). Also find the point of division.
How to lay out the answer. Follow the frame, then write it in your own words.
- 1 · Write what is given and what is to be found. Given: A(−1, −6) and B(5, 3). To find: the ratio in which the x-axis divides AB, and the point P.
- 2 · Write the formula or theorem. Let the ratio be k : 1. P = ((kx₂ + x₁)/(k + 1), (ky₂ + y₁)/(k + 1)).
- 3 · Use y = 0.
- P is on the x-axis, so its y-coordinate is 0.
- (k × 3 + 1 × (−6))/(k + 1) = 0
- 3k − 6 = 0, so k = 2. The ratio is 2 : 1.
- 4 · Find the point. x = (2 × 5 + 1 × (−1))/3 = 9/3 = 3, so P is (3, 0).
- 5 · Check and box the answer. y = (2 × 3 + 1 × (−6))/3 = 0, as needed. Answer: ratio 2 : 1, point (3, 0).
Scoring tip: Write 'on the x-axis, y = 0' in words. That one line earns the method mark.
