Question

find the ratio in which the points (-3,p) divides the line segment joining the points a(-5,-4) and b(-2,-3) in the ratio k:1​

Answer 1

Answer:

The ratio is 2:1 and point p is -10/3

Answer 2

Given :

• A point (-3, p) divides the line segment joining points (-5, -4) and (-2, -3) in the ratio  k : 1

To find :

• Ratio in which the line segment is divided; k : 1 = ?

Formulae required :

• Section formula

The section formula give the coordinates of point (x, y) which divides the line segment joining points ( x₁, y₁) and ( x₂, y₂) in in the ratio m : n.

$\red{\bigstar}\boxed{\sf{(x\;,\;y)=\left(\dfrac{m\;x_2+n\;x_1}{m+n}\;,\;\dfrac{m\;y_2+n\;y_1}{m+n}\right)}}$

Solution :

Using section formula

$\longrightarrow\sf{(-3\;,\;p)=\left(\dfrac{(k)(-2)+(1)(-5)}{(k+1)}\;,\;\dfrac{(k)(-3)+(1)(-4)}{(k+1)}\right)}$

Comparing LHS and RHS

$\longrightarrow\sf{-3=\dfrac{(k)(-2)+(1)(-5)}{(k+1)}}$

$\longrightarrow\sf{-3\;k-3=-2\;k+(-5)}$

$\longrightarrow\sf{-3\;k-3=-2\;k-5}$

$\longrightarrow\sf{-3+5=-2\;k+3\;k}$

$\longrightarrow\underbrace{\boxed{\underline{\underline{\large{\red{\sf{\;\;\;\;\;k=2\;\;\;\;}}}}}}}$

therefore,

• Ratio in which Line segment is divided is 2 : 1