Question

please solve my problem fast it's very urgent​

Answer 1

AnsWer :

32.

Given :

• We have point A (-3 ,6) and B ( 2,1) in the ratio 3 : 2.
• We have equation 3x -8y +k = 0.

Required Concept :

$\blacksquare \tt \: Section \: formula$

$\tt \bullet \: x = \frac{m_2x_1 + m_1 x_2 }{m_2 + m_1}$

$\tt \bullet \: y = \frac{m_2y_1 + m_1 y_2 }{ m_2 + m_1 }$

Solution :

For Point A.

• x1 = -3.
• y1 = 6.

For point B.

• x2 = 2.
• y2 = 1.

Now, Putting the value in Section formula, We get.

$\tt \implies x = \frac{m_2x_1 + m_1 x_2 }{m_2 + m_1}$

$\implies \tt x = \frac{2( - 3) + 3(2)}{5}$

$\implies \tt x = \frac{0}{5}$

$\implies \tt x = 0.$

$\rule{150}1$

$\tt \implies y = \frac{m_2y_1 + m_1 y_2 }{ m_2 + m_1 }$

$\tt\implies y = \frac{3(6) + 2(1)}{5}$

$\tt\implies y = \frac{20}{5}$

$\tt\implies y = 4.$

It means, Point P which is Divided in Radio 3 : 2 be P( 0 , 4 ).

$\rule{200}3$

Now, Let's Putting the value of x and y in given equation, We get.

$\implies\tt3x - 8y + k = 0.$

$\implies\tt3(0) - 8(4) + k = 0.$

$\implies\tt - 32 = - k.$

$\implies\tt k = 32.$

Therefore,the value of k be 32.