A (1, 2) and B (2, 3) are the given points. F | vedclass

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(D) Given the condition $C - A - B$, point $A$ lies between $C$ and $B$.From $2 AC = 3 AB$, we have the ratio $\frac{AC}{AB} = \frac{3}{2}$.Since $A$

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$(-0.5, 0.5)$

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(D) Given the condition $C - A - B$, point $A$ lies between $C$ and $B$.From $2 AC = 3 AB$, we have the ratio $\frac{AC}{AB} = \frac{3}{2}$.Since $A$ divides the segment $\overline{CB}$ internally in the ratio $3:2$, we use the section formula.Let $C = (x_1, y_1)$ and $B = (2, 3)$. The point $A(1, 2)$ divides $\overline{CB}$ in the ratio $m:n = 3:2$.Using the section formula: $A = \left( \frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n} \right)$.$1 = \frac{3(2) + 2(x_1)}{3+2} \implies 5 = 6 + 2x_1 \implies 2x_1 = -1 \implies x_1 = -0.5$.$2 = \frac{3(3) + 2(y_1)}{3+2} \implies 10 = 9 + 2y_1 \implies 2y_1 = 1 \implies y_1 = 0.5$.Thus, the coordinates of $C$ are $(-0.5, 0.5)$.

$A (1, 2)$ and $B (2, 3)$ are the given points. Find the point $C \in \overleftrightarrow{AB}$ such that $C - A - B$ and $2 AC = 3 AB$.

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