Question

Ir 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
(c) 2
(d) 1
(6) 2
​

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,

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

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

$\implies\bf{k=\dfrac{11}{3}}$

$\rule{200}2$

• 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

Answer:

k = 11/3

Step-by-step explanation:

Provided :-

• Point A = 2 , - 2

• Points B = 7 , 4

• Points P = k , 0

Now to solve this question we have to use section formula

( internal division )

If the line segment is divided in the ratio m:n internally

$x = \dfrac{nx_1 + mx_2}{m + n} \: y = \dfrac{ny_1 + my_2}{m + n}$

( external division )

If the line segment is divided in the ratio m:n externally

$x = \dfrac{nx_1 - mx_2}{n - m} \: y = \dfrac{ny_1 - my_2}{n - m}$

Now as it is not mentioned if point p is divided externally or internally we will verify it using the y coordinate ( as it's given )

$0 = \dfrac{ny_1 + my_2}{m + n}$

$0 = \dfrac{(2)(-2) + (1)(4)}{3}$

$0 = \dfrac{(-4) + 4}{3}$

So it divides internally

Now x coordinate / k

$k = \dfrac{nx_1 + mx_2}{m + n}$

$= \dfrac{(2)(2) +(1)( 7}){3}$

$= \dfrac{4 + 7}{3}$

$= \dfrac{11}{3}$