Question

in what ratio is the line joining the points (4,2) and (3,-5), divided by x axis​

Answer 1

Answer:

Step-by-step explanation:

let A ( 4,2)

B ( 3, -5)

given the line AB is divided by x-axis

let the point P( a, 0)

let ratio be m:n

by section formula

(x,y) = ( (mx₂ + nx₁) / (m+n) , (my₂ + ny₁) / (m+ n) )

equating with y

0 = (my₂ + ny₁) / (m+ n) )

0 = (my₂ + ny₁)

0 = m (-5) + n(2)

5m = 2n

m/n = 2/5

m:n = 2:5

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Answer 2

Answer:

P (x,0)= (26/7 , 0)

and ratio in which AB is divided is 2:5.

Step-by-step explanation:

Given , A (4,2) and B (3,-5)

Therefore ,

x1=4

y1=2

x2=3

y2=-5

Let point of intersection be P (x,y)

we know P is on x-axis , therefore P = (x,0)

Let the ratio in which it is divided be m1:m2

0= (m1y2+m2y1)/(m1+m2)

Transposing (m1+m2)

we get ,

0= m1y2+m2y1

0= m1 (-5) + m2 (2)

5m1= 2 m2

=> m1/m2= 2/5

therefore ratio = m1:m2= 2:5

now , using this to find x-co-ordinate of P

x= (m1x2+m2x1)/(m1+m2)

x= ( (2 x 3) + (5 x4)) / (2+5)

x= (6+20)/7

x= 26/7

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