The line segment joining A(2, -7) and B(6, 5) | vedclass

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Question

(A) The points $P, Q, R$ divide the line segment $AB$ into $4$ equal parts. Thus,$AP = PQ = QR = RB = k$ (let).$P$ divides $AB$ in the ratio $1:3$,$Q$

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$(4, -1)$

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(A) The points $P, Q, R$ divide the line segment $AB$ into $4$ equal parts. Thus,$AP = PQ = QR = RB = k$ (let).$P$ divides $AB$ in the ratio $1:3$,$Q$ divides $AB$ in the ratio $2:2$ (or $1:1$),and $R$ divides $AB$ in the ratio $3:1$.Since $Q$ is the midpoint of $AB$,its coordinates are $\left( \frac{2+6}{2}, \frac{-7+5}{2} \right) = (4, -1)$.$P$ is the midpoint of $AQ$. The coordinates of $A$ are $(2, -7)$ and $Q$ are $(4, -1)$.Coordinates of $P = \left( \frac{2+4}{2}, \frac{-7-1}{2} \right) = (3, -4)$.$R$ is the midpoint of $QB$. The coordinates of $Q$ are $(4, -1)$ and $B$ are $(6, 5)$.Coordinates of $R = \left( \frac{4+6}{2}, \frac{-1+5}{2} \right) = (5, 2)$.The midpoint of $PR$ is $\left( \frac{3+5}{2}, \frac{-4+2}{2} \right) = (4, -1)$.

The line segment joining $A(2, -7)$ and $B(6, 5)$ is divided into $4$ equal parts by the points $P, Q$ and $R$ such that $AP = PQ = QR = RB$. The midpoint of $PR$ is

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