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Points on a Cartesian Plane

Three points ...

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

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Solution

The correct option is B
Given, AB = 2BC
AB : BC = 2 : 1
Let C BE (h, k), then
= (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 = and k = - 8 (or) h =; k = 2
C = or
Option(b)

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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

The correct option is B Given, AB = 2BCAB : BC = 2 : 1Let C BE (h, k), then= (6, - 3) [B may divide AC internally or externally]2h + 1 = 18 and 2k + 7 = - 9(or) 2h - 1 = 6 , 2k - 7 = - 32h = 17 and 2k = - 16 (or) 2h = 7, 2k = 4h = and k = - 8 (or) h =; k = 2C = or Option(b)

The correct option is B
Given, AB = 2BC
AB : BC = 2 : 1
Let C BE (h, k), then
= (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 = and k = - 8 (or) h =; k = 2
C = or
Option(b)