If P(1, 12) divides the line segment overline | vedclass

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(A) Let the coordinates of $B$ be $(x, y)$.Given that $P(1, 12)$ divides the line segment $AB$ in the ratio $m:n = 2:1$,where $A(x_1, y_1) = (3, 8)$ a

Vedclass · Accepted Answer

$(0, 14)$

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(A) Let the coordinates of $B$ be $(x, y)$.Given that $P(1, 12)$ divides the line segment $AB$ in the ratio $m:n = 2:1$,where $A(x_1, y_1) = (3, 8)$ and $B(x_2, y_2) = (x, y)$.Using the section formula: $P(x, y) = \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right)$.Substituting the values: $1 = \frac{2(x) + 1(3)}{2+1} \implies 1 = \frac{2x + 3}{3} \implies 3 = 2x + 3 \implies 2x = 0 \implies x = 0$.Similarly,$12 = \frac{2(y) + 1(8)}{2+1} \implies 12 = \frac{2y + 8}{3} \implies 36 = 2y + 8 \implies 2y = 28 \implies y = 14$.Thus,the coordinates of $B$ are $(0, 14)$.

If $P(1, 12)$ divides the line segment $\overline{AB}$ starting from $A$ in the ratio $2:1$ and $A(3, 8)$,then the coordinates of $B$ are $\ldots \ldots$

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