Question
Three points A, B and C are collinear such that AB = 2BC. If the coordinates of the points A and B are (1, 7) and (6, -3) respectively, then the coordinates of the point C can be
Answer: Option B
:
B
Given, AB = 2BC
AB : BC = 2 : 1
Let C BE (h, k), then
(2h±12±1;2k±72±1) = (6, - 3) [B may divide AC internally or externally]
2h + 1 = 18 and 2k + 7 = - 9
(or) 2h - 1 = 6 , 2k - 7 = - 3
2h = 17 and 2k = - 16 (or) 2h = 7, 2k = 4
h = 172 and k = - 8 (or) h = 72; k = 2
C = (172;−8) or (172;2)
Option(b)
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:
B
Given, AB = 2BC
AB : BC = 2 : 1
Let C BE (h, k), then
(2h±12±1;2k±72±1) = (6, - 3) [B may divide AC internally or externally]
2h + 1 = 18 and 2k + 7 = - 9
(or) 2h - 1 = 6 , 2k - 7 = - 3
2h = 17 and 2k = - 16 (or) 2h = 7, 2k = 4
h = 172 and k = - 8 (or) h = 72; k = 2
C = (172;−8) or (172;2)
Option(b)
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