Question

If A = (-4, 3) and B = (8, -6) (i) Find the length of AB (ii) In what ratio is the line joining A and B, divided by the x-axis?

Answer 1

with the help of distance formula we can find AB AND with the help of section formula we can find ratio

Answer 2

The Length AB is 15 unit.

The line joining A and B, divided by the x-axis in the ratio m : n = 1 : 2

Step-by-step explanation:

Given:

Let Point P ( x , 0 )on X-axis divides Segment AB in the ratio = m : n (say)

On X-axis y = 0

point A( x₁ , y₁) ≡ (-4 , 3)  

point B( x₂ , y₂) ≡ (8 , -6)  

To Find:  

l(AB) = ?

point P( x , 0) ≡ ?  

Solution:

Distance AB by distance formula we have

$l(AB) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}$

Substituting we get

$l(AB) = \sqrt{((8--4)^{2}+(-6-3)^{2} )}=\sqrt{((12)^{2}+(9)^{2} )}=\sqrt{225}=15\ unit$

IF a Point P divides Segment AB internally in the ratio m : n, then the Coordinates of Point P is given by Section Formula as

$x=\dfrac{(mx_{2} +nx_{1}) }{(m+n)}\\ \\and\\\\y=\dfrac{(my_{2} +ny_{1}) }{(m+n)}$

Substituting the values we get

$0=\dfrac{(m(-6) +n(3))}{(m+n)}\\\\\therefore 6m=3n\\\\\therefore \dfrac{m}{n}=\dfrac{1}{2}$

The line joining A and B, divided by the x-axis in the ratio m : n = 1 : 2.