Question

Find the ratio in which the point p(3/4,5/12)divides the line segment joining the point a(1/2,3/2)b(2,-5)

Answer 1

Answer:

The required ratio is 3 : 7.

Step-by-step explanation:

Let the ratio be k : 1.

Now, using the section formula, we get

(3/4, 5/12) = ( {2×k + k × 1/2} / k+1 ), ( {-5×1 + 1 × 3/2} / k+1 )

(3/4, 5/12) = ( 2k + k/2 / k+1 ), ( -5 + 3/2 / k+1 )

3/4 = (2k + k/2) / k+1

3/4 = (4k+k / 2) / k+1

(4k+k / 2) × 4 = 3 × (k+1)

(4k+k) × 2 = 3k+3

8k+2k = 3k+3

10k - 3k = 3

7k = 3

i.e., k : 1 = 3 : 7

So, the point P (3/4, 5/12) divides the line segment joining the points A (1/2, 3/2) and B (2, -5) in the ratio 3 : 7.

Hope it helps you!