Question

find the coordinates of the point which divides the line segment joining the points A(- 6,10) and B(3, - 8) in the ratio 2:7​

Answer 1

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Answer 2

The required point is (-4,6)

Step-by-step explanation:

given points A(-6,10) , B(3,8)

here ,

$x_1= -6\\y_1=10\\x_2=3\\ y_1=-8$

the point divides the line in the ratio 2:7

therefore , $m_1=2 , m_2=7$

using the section formula

$\left ( \frac{m_1x_2+m_2x_1}{m_1+m_2}, \frac{m_1y_2+m_2y_1}{m_1+m_2}\right )$

then placing all the values we get

$\left ( \frac{2\times 3 +7\times (-6)}{2+7}, \frac{2\times (-8)+7\times 10}{2+7}\right )\\\\\left ( \frac{6-42}{9},\frac{-16+70}{9} \right )\\\\\left ( \frac{-36}{9}, \frac{54}{9} \right )\\\\\left ( -4,6 \right )$

hence ,The required point is (-4,6)

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