Question

Find the ratio in which the point P(2,x) divides the line joining the points A (-2,2) B (3,7) internally and also find the value of 'x'.

Answer 1

Step-by-step explanation:

P(2,x)=3x-2y/x+y, 7x+2y/x+y

2=3x-2y/x+y

2(x+y)=3x-2y

2x+2y=3x-2y

2x-3x=-2y-2y

-x=-4y

x/y=4/1

x:y=4:1

P(2,x)=7[4]+2[1]/4+1

=28+2/5

=30/5

X=6

Answer 2

Step-by-step explanation:

AnswEr:-

Value of x is 6.

Step by Step Explanation:-

Let us consider that point P(2 , x) divides the line segment joining the points A(-2, 2) and B(3, 7) in the ratio of k:1.

By using Section Formula:-

$:\implies\sf\; \dfrac{m_1\; x_2 + m_2\; x_1}{m_1 \; + \; m_2}\; ,\, \dfrac{m_1\;y_2+m_2\;y_1}{m_1+m_2}$

$\rule{150}3$

$:\implies\sf\;(2,x) = \dfrac{(k)(3) + (1) (-2)}{k + 1}\; ,\; \dfrac{(k)(7) + (1)(2)}{k + 1}$

$:\implies\sf\;(2 , x) = \dfrac{ 3k - 2}{k + 1}\; ,\; \dfrac{7 k + 2}{k + 1}$

$:\implies\sf\;2 = \dfrac{3k - 2}{k + 1}$

$:\implies\sf\; 2 (k + 1) = 3k - 2$

$:\implies\sf\;2k - 3k = -2 - 2$

$:\implies\sf\; - k = - 4$

$:\implies\large\boxed{\sf{\pink{ k = 4}}}$

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The Point (2 ,x) divides the line segment in the ratio of 4:1.

$:\implies\sf\;x = \dfrac{7k + 2}{k + 1}$

Putting the value of k

$:\implies\sf\; x =\dfrac{7(4) + 2}{4 + 1}$

$:\implies\sf\; x = \dfrac{30}{5}$

$:\implies\large\boxed{\sf{\pink{x = 6}}}$

$\rule{150}3$