Question

1. The ratio in which the line 2x + y = 4 divides the line segment joining A (2, −2) and B (3, 7) is 2 : 5.
2. G (4, 3) is the centroid of ΔABC, where A (1, 3), В (4, b), and C (9, 1), then b = 4.

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Neither (i) nor (ii)

Explanation:

⇒ For (i), letting P divide AB in k : 1 gives;

P`((3k + 2)/(k + 1),(7k - 2)/(k + 1))`

Substituting in 2x + y = 4 yields k = `2/9`,

So the ratio is 2 : 9 not 2 : 5

⇒ For (ii), centroid x-coordinate

= `(1 + 4 + 9)/3`

= `14/3` ≠ 4

So b cannot be 4.

Hence, both statements are false.