Find the coordinates of the points of trisect | vedclass

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Question

(A) Let $A = (4, -1)$ and $B = (-2, -3)$. Let $P$ and $Q$ be the points of trisection such that $AP = PQ = QB$.Point $P$ divides $AB$ in the ratio $1:

Vedclass · Accepted Answer

$(2, -5/3)$ and $(0, -7/3)$

Vedclass · Answer

(A) Let $A = (4, -1)$ and $B = (-2, -3)$. Let $P$ and $Q$ be the points of trisection such that $AP = PQ = QB$.Point $P$ divides $AB$ in the ratio $1:2$. Using the section formula $\left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right)$:$x_1 = \frac{1(-2) + 2(4)}{1+2} = \frac{-2+8}{3} = \frac{6}{3} = 2$$y_1 = \frac{1(-3) + 2(-1)}{1+2} = \frac{-3-2}{3} = -\frac{5}{3}$So,$P = (2, -5/3)$.Point $Q$ divides $AB$ in the ratio $2:1$. Using the section formula:$x_2 = \frac{2(-2) + 1(4)}{2+1} = \frac{-4+4}{3} = 0$$y_2 = \frac{2(-3) + 1(-1)}{2+1} = \frac{-6-1}{3} = -\frac{7}{3}$So,$Q = (0, -7/3)$.

Find the coordinates of the points of trisection of the line segment joining $(4, -1)$ and $(-2, -3)$.

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