Exercise 10.1

To divide a line segment \[\mathbf{AB}\]in the ratio\[\mathbf{5}\text{ }:\text{ }\mathbf{6}\], draw a ray \[\mathbf{AX}\]such that \[\angle \mathbf{BAX}\] is an acute angle, then draw a ray \[\mathbf{BY}\]parallel to \[\mathbf{AX}\]and the points \[{{\mathbf{A}}_{\mathbf{1}}},\text{ }{{\mathbf{A}}_{\mathbf{2}}},\text{ }{{\mathbf{A}}_{\mathbf{3}}},\text{ }\ldots \]and \[{{\mathbf{B}}_{\mathbf{1}}},\text{ }{{\mathbf{B}}_{\mathbf{2}}},\text{ }{{\mathbf{B}}_{\mathbf{3}}},\text{ }\ldots \]are located at equal distances on ray \[\mathbf{AX}\]and\[\mathbf{BY}\], respectively. Then the points joined are \[\left( \mathbf{A} \right)\text{ }{{\mathbf{A}}_{\mathbf{5}}}~\mathbf{and}\text{ }{{\mathbf{B}}_{\mathbf{6}}}~\] \[\left( \mathbf{B} \right)\text{ }{{\mathbf{A}}_{\mathbf{6}}}~\mathbf{and}\text{ }{{\mathbf{B}}_{\mathbf{5}}}~\] \[~\left( \mathbf{C} \right)\text{ }{{\mathbf{A}}_{\mathbf{4}}}~\mathbf{and}\text{ }{{\mathbf{B}}_{\mathbf{5}}}\] \[\left( \mathbf{D} \right)\text{ }{{\mathbf{A}}_{\mathbf{5}}}~\mathbf{and}\text{ }{{\mathbf{B}}_{\mathbf{4}}}\]

\[\left( \mathbf{A} \right)\text{ }{{\mathbf{A}}_{\mathbf{5}}}~\mathbf{and}\text{ }{{\mathbf{B}}_{\mathbf{6}}}\] As per the inquiry, A line portion \[AB\]in the proportion \[5:7\] Along these...

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To divide a line segment \[\mathbf{AB}\]in the ratio\[\mathbf{4}:\mathbf{7}\], a ray \[\mathbf{AX}\]is drawn first such that \[\mathbf{BAX}\]is an acute angle and then points \[{{\mathbf{A}}_{\mathbf{1}}},\text{ }{{\mathbf{A}}_{\mathbf{2}}},\text{ }{{\mathbf{A}}_{\mathbf{3}}},\ldots .\]are located at equal distances on the ray \[\mathbf{AX}\]and the point \[\mathbf{B}\]is joined to \[\left( \mathbf{A} \right)\text{ }{{\mathbf{A}}_{\mathbf{12}}}~\left( \mathbf{B} \right)\text{ }{{\mathbf{A}}_{\mathbf{11}}}~\left( \mathbf{C} \right)\text{ }{{\mathbf{A}}_{\mathbf{10}}}~\left( \mathbf{D} \right)\text{ }{{\mathbf{A}}_{\mathbf{9}}}\]

SOLUTION:- \[\left( \mathbf{B} \right)\text{ }{{\mathbf{A}}_{\mathbf{11}}}\] As per the inquiry, A line section\[~AB\] in the proportion \[4:7\] Thus, \[A:B\text{ }=\text{ }4:7\] Presently, Draw a...

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To divide a line segment \[\mathbf{AB}\]in the ratio\[\mathbf{5}:\mathbf{7}\], first a ray \[\mathbf{AX}\]is drawn so that \[\mathbf{BAX}\]is an acute angle and then at equal distances points are marked on the ray \[\mathbf{AX}\]such that the minimum number of these points is (A) \[\mathbf{8}\](B) \[\mathbf{10}\](C)\[~\mathbf{11}\] (D) \[\mathbf{12}\]

SOLUTION:- \[\left( D \right)\text{ }12\] As indicated by the inquiry, A line fragment \[AB\]in the proportion \[5:7\] In this way, \[A:B\text{ }=\text{ }5:7\] Presently, Draw a beam \[AX\]making an...

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