In what ratio does the point T (3, 0) divide the segment

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In what ratio does the point T (3, 0) divide the segment joining the points S (4, –2) and U (1, 4)?

1. 2 : 1
2. 1 : 2
3. 2 : 3
4. 3 : 2

Correct Option: B

Let point T divide line segment SU in the ratio k : 1.
If the co-ordinates of point T be (x, y) and that of points S an U be (x₁, y₁) and (x₂, y₂) respectively, then

x =	kx₂ + x₁	; y =	ky₂ + y₁
	k + 1		k + 1

∴ 3 =	k × 1 + 1 × 4
	k + 1

⇒ 3k + 3 = k + 4
⇒ 3k – k = 4 – 3
⇒ 2k = 1

⇒ k =	1	= 1 : 2
	2