The points which trisect the line segment joi | vedclass

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Question

(A) Let the points be $A(0, 0)$ and $D(9, 12)$. Let $B$ and $C$ be the points that trisect the line segment $AD$.$(i)$ Point $B$ divides $AD$ in the r

Vedclass · Accepted Answer

$(3, 4), (6, 8)$

Vedclass · Answer

(A) Let the points be $A(0, 0)$ and $D(9, 12)$. Let $B$ and $C$ be the points that trisect the line segment $AD$.$(i)$ Point $B$ divides $AD$ in the ratio $1 : 2$.Using the section formula,the coordinates of $B$ are:$x = \frac{1(9) + 2(0)}{1 + 2} = \frac{9}{3} = 3$$y = \frac{1(12) + 2(0)}{1 + 2} = \frac{12}{3} = 4$So,$B = (3, 4)$.$(ii)$ Point $C$ divides $AD$ in the ratio $2 : 1$.Using the section formula,the coordinates of $C$ are:$x = \frac{2(9) + 1(0)}{2 + 1} = \frac{18}{3} = 6$$y = \frac{2(12) + 1(0)}{2 + 1} = \frac{24}{3} = 8$So,$C = (6, 8)$.Thus,the points are $(3, 4)$ and $(6, 8)$.

The points which trisect the line segment joining the points $(0, 0)$ and $(9, 12)$ are

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