If C is a point on the line segment joining A | vedclass

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Question

(A) Given that $C$ divides the line segment joining $A(-3, 4)$ and $B(2, 1)$ in the ratio $AC : BC = 2 : 1$.Using the section formula, the coordinates

Vedclass · Accepted Answer

$\left(\frac{1}{3}, 2\right)$

Vedclass · Answer

(A) Given that $C$ divides the line segment joining $A(-3, 4)$ and $B(2, 1)$ in the ratio $AC : BC = 2 : 1$.Using the section formula, the coordinates of $C(x, y)$ are given by:$x = \frac{m_1x_2 + m_2x_1}{m_1 + m_2} = \frac{2(2) + 1(-3)}{2 + 1} = \frac{4 - 3}{3} = \frac{1}{3}$$y = \frac{m_1y_2 + m_2y_1}{m_1 + m_2} = \frac{2(1) + 1(4)}{2 + 1} = \frac{2 + 4}{3} = \frac{6}{3} = 2$Thus, the coordinates of $C$ are $\left(\frac{1}{3}, 2\right)$.

If $C$ is a point on the line segment joining $A(-3, 4)$ and $B(2, 1)$ such that $AC = 2BC$, then the coordinates of $C$ are

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