Question

Find the ratio in which the line 2x + 3y - 30 = 0 divides the line segment joining the points ( 3, 4 ) and ( 7, 8). Find also the coordinates of the point of intersection.

Answer 1

Answer:

Step-by-step explanation:

Let the given points be A(3,4) and (7,8)

Given that the line 2x + 3y - 30 = 0 divides the line joining A and B .

Here , we will be using internal sectional formula

i.e.,

Suppose if a point M divides the line joining A(x₁ , y₁) and B (x₂ , y₂ ) in the ratio m: n internally, then the co-ordinates  of M are given by

(mx₂ + nx₁/m+n, my₂ + ny₁/m+n).

Now. let us assume that line intersects line AB at point M.

Let M divides the line joining A and B in the ratio λ:1,

then the coordinates of M are given by

(7λ + 3/λ+1,8λ+4/λ+1)

But M lies on 2x + 3y - 30 = o\0 since it is the point of intersection of 2 lines.

=>2(7λ + 3/λ+1) + 3(8λ+4/λ+1) = 30

=>14λ + 6 + 24λ + 12 = 30λ + 30

=>8λ = 12

=>λ = 12/8 =3/2

Hence the ratio in which the given line divided AB is 3:2.

Co-ordinates of M are (3*7 + 2*3/5 , 3*8 + 2*4/5)

=(27/5, 32/5).

Answer 2

Heyy mate ❤✌✌❤

Here's your Answer....

⤵️⤵️⤵️⤵️⤵️⤵️⤵️

let line divides 2x+3y-5=0 to the segment joining (8,-9) and (2,1) in k:1

let point of intersect be (a,b)

by intersection formula

(a,b)=(2k+8/k+1  , k-9/k+1)

a=2k+8/k+1  and b=k-9/k+1

these point will also lie on line 2x+3y-5=0.hence point will satisfy this equation

2×2k+8/k+1 + 3×k-9/k+1 -5 =0

4k+16+3k-27-5k-5=0

2k-16=0

k=8

ratio will be 8:1

coordinate will be x=2k+8/k+1=24/9 and y=k-9/k+1=-1/9
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