Question

find the ratio in which line segment joining A (1,-5) and B (-4,5) is divided by the x-axis. Also find the coordinates of the point of division. ​

Answer 1

Answer:

1:1 at (-3/2,0)

Step-by-step explanation:

considering X axis, Y co-ordinate is 0

Hence assume the point dividing the line as (x,0) divides the line in ratio a:1

A              k            T            1                  B

(1,-5)                   (x,0)                           (-4,5)

(a,b)          m       (x,y)            n             (c,d)

Use section formula

P ( x , y ) = ( c ⋅ m + a ⋅ n  , d ⋅ m + b ⋅ n)/( m + n )

y=(m.d+n.b) / (m+n)

0=[(k*5)+(1*-5)]/[k+1]

0=5k-5

k=1

x=( c ⋅ m + a ⋅ n)/( m + n )

 = (k*-4)+(1*1)/(k+1)

= (-4k+1)/(k+1)

= (-4+1)/(1+1)       (Since k=1)

= -3/2

The point T(x,0) is (-3/2,0)

Answer 2

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