Question

Find the ratio in which the point P[3/4],[5/12]

Answer 1

Step-by-step explanation:

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ANSWER

Let point P divide AB in the ratio 1:k

[REF.image]

Then, by ratio formula,

( 43, 125 )≡ ⎝

⎜

⎛

k+1

k(

2

1

)+1(2)

,

k+1

k(

2

3

)+1(−5)

⎠

⎟

⎟

⎟

⎞

Equating x and y coordinates, we get

k+1

k/2+2

=

4

3

,

k+1

3k/2−5

=

12

5

⇒2k+8=3k+3,18k−60=5k+5

⇒k=5

Answer 2

▪︎Let k :1 be the ratio in which the point P (3/4, 5/12) divides the line segment joining the points A (1/2, 3/2) and B (2, -5). Then

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

Equating x and y coordinates, we get ,

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

=> 2k+8 = 3k + 3, 18k-60 = 5k+5

=> {k = 5}

Hence P divides AB in the ratio 1:5

▪︎The required ratio is 1: 5.

♥️. HOPE THIS WILL HELP YOU BUDDY....