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  • Find the ratio in which the y-axis divides the line segment joining the points (–1, – 4) and (5, – 6). Also, find the coordinates of the point of intersection    

Find the ratio in which the y-axis divides the line segment joining the points (–1, – 4) and (5, – 6). Also, find the coordinates of the point of intersection

 

 

 

 
 
 
 
 

Answers (1)

Let the point be (5.-6)    B(-1,-4)

Point P on the x-axis so its coordinates are (0,y)

Let the ratio be k:1

hence    \\m_1 = k \\m_2 = 1

(x_1,y_1) = (5,-6),\qquad (x_2,y_2) = (-1,-4),\qquad (x,y) = (0,y)

x = \frac{m_1x_2 + m_2x_1}{m_1 + m_2}

0 = \frac{k(-1) + 1\times 5}{k + 1}\Rightarrow k = 5

y= \frac{m_1y_2 + m_2y_1}{m_1 + m_2} = \frac{k(-4) + 1(-6)}{k + 1}

y= \frac{5(-4) + 1(-6)}{5 + 1}\qquad (\text{Put value of k = 5})

y= \frac{-20-6}{6} = \frac{-13}{3}

Hence the coordinate of point P is \left (0,\frac{-13}{3} \right )

Posted by

Safeer PP

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