In what ratio does the point (-4, 6) divide t | vedclass

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(A) Let the point $P(-4, 6)$ divide the line segment joining $A(-6, 10)$ and $B(3, -8)$ in the ratio $m_{1}: m_{2}$.Using the section formula,the coor

Vedclass · Accepted Answer

$2: 7$

Vedclass · Answer

(A) Let the point $P(-4, 6)$ divide the line segment joining $A(-6, 10)$ and $B(3, -8)$ in the ratio $m_{1}: m_{2}$.Using the section formula,the coordinates of $P$ are given by:$P(x, y) = \left( \frac{m_{1}x_{2} + m_{2}x_{1}}{m_{1} + m_{2}}, \frac{m_{1}y_{2} + m_{2}y_{1}}{m_{1} + m_{2}} \right)$Substituting the values:$(-4, 6) = \left( \frac{3m_{1} - 6m_{2}}{m_{1} + m_{2}}, \frac{-8m_{1} + 10m_{2}}{m_{1} + m_{2}} \right)$Equating the $x$-coordinates:$-4 = \frac{3m_{1} - 6m_{2}}{m_{1} + m_{2}}$$-4(m_{1} + m_{2}) = 3m_{1} - 6m_{2}$$-4m_{1} - 4m_{2} = 3m_{1} - 6m_{2}$$2m_{2} = 7m_{1}$$\frac{m_{1}}{m_{2}} = \frac{2}{7}$Thus,the ratio is $2: 7$.

In what ratio does the point $(-4, 6)$ divide the line segment joining the points $A(-6, 10)$ and $B(3, -8)$?

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