A (3, 3) and B (6, 1) are the given points. F | vedclass

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(A) Given points are $A(3, 3)$ and $B(6, 1)$.Let the coordinates of point $C$ be $(x, y)$.The condition $A-B-C$ implies that $B$ lies between $A$ and

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$(15, -5)$

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(A) Given points are $A(3, 3)$ and $B(6, 1)$.Let the coordinates of point $C$ be $(x, y)$.The condition $A-B-C$ implies that $B$ lies between $A$ and $C$.The condition $3 AB = BC$ implies that the ratio $AB : BC = 1 : 3$.Since $B$ divides $AC$ externally in the ratio $1 : 3$ (or internally in the ratio $1 : 3$ if we consider $B$ as a point on the segment $AC$),we use the section formula.Alternatively,using vectors: $\vec{B} - \vec{A} = (6-3, 1-3) = (3, -2)$.Since $BC = 3 AB$,the vector $\vec{BC} = 3 \vec{AB} = 3(3, -2) = (9, -6)$.Thus,$\vec{C} = \vec{B} + \vec{BC} = (6, 1) + (9, -6) = (15, -5)$.

$A (3, 3)$ and $B (6, 1)$ are the given points. Find the point $C$ on the line $\overleftrightarrow{AB}$ such that $A-B-C$ and $3 AB = BC$.

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