Draw $\overline{ AB }$ of length $7 \,cm$ and obtain a point $M$ on $\overline{ AB }$ such that $AM : AB = 2 : 5$. Write the steps of construction.
(N/A) Steps of construction:
$1$. Draw a line segment $\overline{ AB }$ of length $7 \,cm$ using a ruler.
$2$. Draw an acute angle $\angle BAX$ at point $A$ with the line segment $\overline{ AB }$.
$3$. Mark $5$ points $A_1, A_2, A_3, A_4, A_5$ on the ray $AX$ such that $AA_1 = A_1A_2 = A_2A_3 = A_3A_4 = A_4A_5$ using a compass.
$4$. Join $A_5$ to $B$.
$5$. Through point $A_2$,draw a line parallel to $A_5B$ intersecting $\overline{ AB }$ at point $M$.
$6$. Thus,$M$ is the required point on $\overline{ AB }$ such that $AM : AB = 2 : 5$.
$1$. Draw a line segment $\overline{ AB }$ of length $7 \,cm$ using a ruler.
$2$. Draw an acute angle $\angle BAX$ at point $A$ with the line segment $\overline{ AB }$.
$3$. Mark $5$ points $A_1, A_2, A_3, A_4, A_5$ on the ray $AX$ such that $AA_1 = A_1A_2 = A_2A_3 = A_3A_4 = A_4A_5$ using a compass.
$4$. Join $A_5$ to $B$.
$5$. Through point $A_2$,draw a line parallel to $A_5B$ intersecting $\overline{ AB }$ at point $M$.
$6$. Thus,$M$ is the required point on $\overline{ AB }$ such that $AM : AB = 2 : 5$.
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