If P (9a-2, -b) divides the line segment join | vedclass

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(B) Given that point $P(9a-2, -b)$ divides the line segment joining $A(3a+1, -3)$ and $B(8a, 5)$ in the ratio $m_1:m_2 = 3:1$.Using the section formul

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$1, -3$

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(B) Given that point $P(9a-2, -b)$ divides the line segment joining $A(3a+1, -3)$ and $B(8a, 5)$ in the ratio $m_1:m_2 = 3:1$.Using the section formula,the coordinates of point $P$ are given by:$P(x, y) = \left( \frac{m_1x_2 + m_2x_1}{m_1+m_2}, \frac{m_1y_2 + m_2y_1}{m_1+m_2} \right)$Equating the $x$-coordinates:$9a - 2 = \frac{3(8a) + 1(3a+1)}{3+1}$$9a - 2 = \frac{24a + 3a + 1}{4}$$4(9a - 2) = 27a + 1$$36a - 8 = 27a + 1$$36a - 27a = 1 + 8$$9a = 9 \implies a = 1$Equating the $y$-coordinates:$-b = \frac{3(5) + 1(-3)}{3+1}$$-b = \frac{15 - 3}{4}$$-b = \frac{12}{4}$$-b = 3 \implies b = -3$Thus,the values are $a = 1$ and $b = -3$.

If $P (9a-2, -b)$ divides the line segment joining $A (3a+1, -3)$ and $B (8a, 5)$ in the ratio $3:1$,find the values of $a$ and $b$.

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