# Find the Ratio in Which the Point P(X, 2) Divides the Line Segment Joining the Points A(12, 5) and B(4, −3). Also, Find the Value of X. - Mathematics

Find the ratio in which the point P(x, 2) divides the line segment joining the points A(12, 5) and B(4, −3). Also, find the value of x.

#### Solution 1

Let the point P (x, 2) divide the line segment joining the points A (12, 5) and B (4, −3) in the ratio k:1.

Then, the coordinates of P are ((4k+12)/(k+1),(-3k+5)/(k+1))

Now, the coordinates of P are (x, 2).

therefore (4k+12)/(k+1)=x and (-3k+5)/(k+1)=2

(-3k+5)/(k+1)=2

-3k+5=2k+2

5k=3

k=3/5

Substituting k=3/5 " in"  (4k+12)/(k+1)=x

we get

x=(4xx3/5+12)/(3/5+1)

x=(12+60)/(3+5)

x=72/8

x=9

Thus, the value of x is 9.

Also, the point P divides the line segment joining the points A(12, 5) and (4, −3) in the ratio 3/5:1  i.e. 3:5.

#### Solution 2

Let k be the ratio in which the point P(x,2)  divides the line joining the points

A(x_1 =12, y_1=5) and B(x_2 = 4, y_2 = -3 ) . Then

x= (kxx4+12)/(k+1) and 2 = (kxx (-3)+5) /(k+1)

Now,

 2 = (kxx (-3)+5)/(k+1) ⇒ 2k+2 = -3k +5 ⇒ k=3/5

Hence, the required ratio is3:5 .

Concept: Section Formula
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#### APPEARS IN

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