The mid-point of the line joining the points (–10, 8) and (–6, 12) divides the line joining the points (4, –2) and (– 2, 4) in the ratio -Maths 9th

The mid-point of the line joining the points (–10, 8) and (–6, 12) divides the line joining the points (4, –2) and (– 2, 4) in the ratio -Maths 9th
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(d) 2 : 1 externallyThe mid-point of the line joining the points (–10, 8) and (– 6, 12) is\(\bigg(rac{-10+(-6)}{2},rac{8+12}{2}\bigg)\), i.e., (–8, 10).Let (–8, 10) divide the join of (4, –2) and (–2, 4) in the ratio k : 1. Then, –8 = \(rac{-2k+4}{k+1}\) and 10 = \(rac{4k-2}{k+1}\)⇒ – 8k – 8 = – 2k + 4 ⇒ – 6k = 12 ⇒ k = –2 Since the value of k is negative, it is a case of external division and the ratio is 2 : 1.
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