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

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Given, AB = 2BC

AB : BC = 2 : 1

Let C BE (h, k), then

$(\frac{2h\pm 1}{2\pm 1};\frac{2k\pm 7}{2\pm 1})$ = (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 = $\frac{17}{2}$ and k = - 8 (or) h = $\frac{7}{2}$; k = 2

C = $(\frac{17}{2};-8)$ or $(\frac{17}{2};2)$

Option(b)