Question

P(-2,12) divides line segment AB joining A(4,6) and B(-12,22) in ratio
​

Answer 1

Answer:

BP is 5 and PA is 3 ratio is 5:3

Step-by-step explanation:

Bx-Px=-12--2=10

By-Py=22-12=10

Px-Ax=-2-4=-6

Py-Ay=12-6=6

10:6 = 5:3

Answer 2

Answer:

The point P(-2,12) divides the line segment AB in the ratio 3:5.

Step-by-step explanation:

Given: Point P(-2,12) divides the line segment AB joining the points A(4,6) and B(-12,22) in some ratio.

Let the point P divides the line segment AB in the ratio m:1.

w.k.t., point which divides a line segment joining the points (x₁,y₁) and (x₂,y₂) in the ratio m:n is $\tt{ (\dfrac{mx_{2}+nx_{1}}{m+n} \ , \ \dfrac{my_{2}+ny_{1}}{m+n}) }$.

⇒ Co-ordinates of point P are $\tt{ (\dfrac{m(-12)+1(4)}{m+1} \ , \ \dfrac{m(22)+1(6)}{m+1}) }$.

⇒ P ≡ $\tt{ (\dfrac{-12m+4}{m+1} \ , \ \dfrac{22m+6}{m+1}) }$

But co-ordinates of point P are (-2,12).

$\tt{ \implies -2 = \dfrac{-12m+4}{m+1} }$

$\tt{ \implies -2(m+1) = -12m+4 }$

$\tt{ \implies -2m-2 = -12m+4 }$

$\tt{ \implies 10m = 6 }$

$\tt{ \implies m = \dfrac{3}{5} }$

Also, $\tt{ 12 = \dfrac{22m+6}{m+1} }$

$\tt{ \implies 12(m+1) = 22m+6 }$

$\tt{ \implies 12m+12 = 22m+6 }$

$\tt{ \implies -10m = -6 }$

$\tt{ \implies m = \dfrac{3}{5} }$

⇒ The ratio in which the point P divides the line segment AB is 3:5.