If A (-2,-1) and B (7,8), then find the coord | vedclass

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(A) Let the points of trisection be $P$ and $Q$. Point $P$ divides $AB$ in the ratio $1:2$ and point $Q$ divides $AB$ in the ratio $2:1$.Using the sec

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$(1,2), (4,5)$

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(A) Let the points of trisection be $P$ and $Q$. Point $P$ divides $AB$ in the ratio $1:2$ and point $Q$ divides $AB$ in the ratio $2:1$.Using the section formula,$P = \left( \frac{m_1x_2 + m_2x_1}{m_1 + m_2}, \frac{m_1y_2 + m_2y_1}{m_1 + m_2} \right)$.For point $P$ $(m_1=1, m_2=2)$: $P = \left( \frac{1(7) + 2(-2)}{1+2}, \frac{1(8) + 2(-1)}{1+2} \right) = \left( \frac{7-4}{3}, \frac{8-2}{3} \right) = \left( \frac{3}{3}, \frac{6}{3} \right) = (1, 2)$.For point $Q$ $(m_1=2, m_2=1)$: $Q = \left( \frac{2(7) + 1(-2)}{2+1}, \frac{2(8) + 1(-1)}{2+1} \right) = \left( \frac{14-2}{3}, \frac{16-1}{3} \right) = \left( \frac{12}{3}, \frac{15}{3} \right) = (4, 5)$.Thus,the coordinates of the trisection points are $(1, 2)$ and $(4, 5)$.

If $A (-2,-1)$ and $B (7,8),$ then find the coordinates of the trisection points of $\overline{ AB }$.

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