Chapter: Co-ordinate Geometry· Mathematics Part 2 (Geometry)
Answer: Ratio 2 : 1; point of division (4, 0)
Let the X-axis divide AB at P in the ratio m : n. Every point on the X-axis has y co-ordinate 0, so P = (x, 0).
By section formula for y: \(0 = \dfrac{m(-3) + n(6)}{m + n}\) \(\therefore -3m + 6n = 0\) \(\therefore 3m = 6n\) \(\therefore m : n = 2 : 1\).
Then \(x = \dfrac{2(8) + 1(-4)}{2 + 1} = \dfrac{16 - 4}{3} = \dfrac{12}{3} = 4\).
\(\therefore\) The X-axis divides AB in the ratio 2 : 1 at the point P(4, 0).