Question

9.
If the point P(k, 0) divides the line segment joining the points A(2, -2) and
B(-7, 4) in the ratio 1:2, then the value of k is
(a) 1
(b) 2
(C) -2. (d) -1​

Answer 1

Answer:-

The point that divides the line = P (k,0)

First point joining the line = A (2,-2)

The second point joining the line = B (-7,4)

Ratio = 1:2

The section formula will be used to find the value of k.

$\dag\bf{(x,y)=\bigg(\dfrac{m_1x_2+m_2x_1}{m_1+m_2},\dfrac{m_1y_2+m_2y_1}{m_1+m_2}\bigg)}$

Substituting the values,

$\implies\sf{k=\dfrac{(1)(-7)+(2)(2)}{1+2}}$

$\implies\sf{k=\dfrac{-7+4}{3}}$

$\implies\bf{k=\dfrac{3}{3}}$

$\implies\bf{k=1}$

$\rule{200}2$

SOME MORE IMPORTANT FORMULAS:-

The midpoint formula

$\dag\sf{\bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)}$

The distance formula

$\dag\sf{\sqrt{{(x_2-x_1)}^{2}+{(y_2-y_1)}^{2}}}$

The Centroid formula

$\dag\sf{\bigg(\dfrac{x_1+x_2+x_3}{3},\dfrac{y_1+y_2+y_3}{3}\bigg)}$

$\rule{200}2$

Answer 2

$\tt{\huge{\orange {Hello!!! }}} ITz$

QUESTION :

If the point P(k, 0) divides the line segment joining the points

A(2, -2) and B(-7, 4) in the ratio 1:2, then the value of k is .....

(a) 1

(b) 2

(C) -2

(d) -1

SOLUTION :

The Line Segment Joining AB divides the distance between them in the ratio 1 : 2 at point P.

Using the internal Bisector Fromula,

Coordinates of P :

( x , y ) = [ { m 1 } × { x 2} + { m 2 } × { x 1 } / { m 1 } + { m 2 } ] , [ [ { m 1 } × { x y} + { m 2 } × { x y } / { m 1 } + { m 2 } ]

y = 0

X => K

=> K = [ { 1 } × { -7 } + 2 { 2 } ] / [ 2 + 1 ]

=> K = [ - 3 ] / [ 3 ] = -1

Hence the value of K is -1.

=> K =