Question

Find the ratio in which point (x, 2) divides the line segment joining points (-3, -4) and (3, 5). Also find the value of x.

Answer 1

Ratio is 2:1 & Value of x is 1

Solution:

Given:

• Points of line (-3,-4) & (3,5)
• And Point in the line (x,2)

To find : Value of X & Ratio of division.

Let the point (x,2) divide the line in k:1 ratio.

∴ x = (3k -3)/(k+1) [from section formula]

And

2 = (5K -4)/(k+1)

⇒ 2(k+1) = 5k - 4

or, 2k + 2 = 5k -4

or, 6 = 3k

or, k = 6/3 = 2

Hence, Ratio is 2:1.

x = (3k -3)/(k+1)

substituting value of k

⇒ x = (3x2 - 3)/(2+1)

or, x = (6-3)/(3)

or, x = 3/3

or, x = 1

Answer 2

Given:

Points of line (-3,-4) & (3,5)

And Point in the line (x,2)

To find : Value of X & Ratio of division.

Let the point (x,2) divide the line in k:1 ratio.

∴ x = (3k -3)/(k+1) [from section formula]

And

2 = (5K -4)/(k+1)

⇒ 2(k+1) = 5k - 4

or, 2k + 2 = 5k -4

or, 6 = 3k

or, k = 6/3 = 2

Hence, Ratio is 2:1.

x = (3k -3)/(k+1)

substituting value of k

⇒ x = (3x2 - 3)/(2+1)

or, x = (6-3)/(3)

or, x = 3/3

or, x = 1