To divide a line segment AB in the ratio p: q | vedclass

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(A) To divide a line segment $AB$ in the ratio $p:q$,we draw a ray $AX$ making an acute angle with $AB$.We then mark $p+q$ points on the ray $AX$ at e

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$p+q$

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(A) To divide a line segment $AB$ in the ratio $p:q$,we draw a ray $AX$ making an acute angle with $AB$.We then mark $p+q$ points on the ray $AX$ at equal distances,say $A_1, A_2, \dots, A_{p+q}$,such that $AA_1 = A_1A_2 = \dots = A_{p+q-1}A_{p+q}$.We join the last point $A_{p+q}$ to $B$.Then,we draw a line parallel to $A_{p+q}B$ through the point $A_p$ to intersect $AB$ at a point $P$.This point $P$ divides the line segment $AB$ in the ratio $p:q$.Therefore,the minimum number of points to be marked on the ray $AX$ is $p+q$.

To divide a line segment $AB$ in the ratio $p: q$ ($p, q$ are positive integers),draw a ray $AX$ so that $\angle BAX$ is an acute angle and then mark points on ray $AX$ at equal distances such that the minimum number of these points is

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