Question

In what ratio does the point P on x axis divide the line segment joining the points A(- 4,5) And B (3,-7) also find the coordinates of the p

Answer 1

Step-by-step explanation:

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Answer 2

The line segment joining the points A(- 4,5) and B (3,-7) on x axis is 5:7 and the coordinate of point P is$(\dfrac{-13}{12} ,0)$

Step-by-step explanation:

Given : The line joining the points A(-4,5)  and B(3,-7) intersect x axis at point P

Let the coordinates of P(x,0)

Therefore as we know by section formula

$(x,y)=(\dfrac{x_1m_2+x_2m_1}{m_1+m_2},\dfrac{y_1m_2+y_2m_1}{m_1+m_2}, )$

Let

$(x,y)=(x,0) \text { , } (x_1,y_1)= (-4,5) \text { and } (x_2,y_2)=(3,-7) \\\\ \text { also }m_1:m_2= k:1$

Substituting the values we get

$y=\dfrac{y_1m_2+y_2m_1}{m_1+m_2} \\\\\Rightarrow 0= \dfrac{5\times 1+ (-7)\times k}{k+1} \\\\\Rightarrow 7k=5\\\\\Rightarrow k=\dfrac{5}{7}$

Therefore the ratio is 5:7

Now

$x= \dfrac{x_1m_2+x_2m_1}{m_1+m_2} =\dfrac{-4\times 7+3\times 5}{7+5} =\dfrac{-13}{12}$

Therefore the coordinates of point P is$(\dfrac{-13}{12} ,0)$

#Learn more

In what ratio is the line joining the points (2,-3) and (5,6) divided by the x axis

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