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Given-the-lines-l-1-x-y-5-and-l-2-y-4x-and-l-3-4x-y-1-0-show-that-l-2-is-perpendicular-to-l-3-find-the-point-coordinates-if-x-2y-5-is-colliner-to-l-1-

Question Number 39127 by Rio Mike last updated on 02/Jul/18 $${Given}\:{the}\:{lines} \\ $$$${l}_{\mathrm{1}} :\:\:{x}\:+\:{y}\:=\:\mathrm{5}\:{and}\:{l}_{\mathrm{2}} :\:{y}\:=\:\mathrm{4}{x} \\ $$$${and}\:{l}_{\mathrm{3}} ;\:\mathrm{4}{x}\:+\:{y}\:−\:\mathrm{1}\:=\mathrm{0} \\ $$$${show}\:{that}\:{l}_{\mathrm{2}\:} \:{is}\:{perpendicular} \\ $$$${to}\:{l}_{\mathrm{3}} . \\…

Given-the-matrices-A-3-5-2-4-and-I-1-0-0-1-find-matrix-B-if-BA-I-find-A-the-reflection-on-the-line-y-x-and-A-the-enlargement-with-matrix-2-0-0-2-

Question Number 39013 by Rio Mike last updated on 01/Jul/18 $${Given}\:{the}\:{matrices} \\ $$$${A}\:=\:\begin{pmatrix}{\mathrm{3}}&{\mathrm{5}}\\{\mathrm{2}}&{\mathrm{4}}\end{pmatrix}\:{and}\:{I}\:=\:\begin{pmatrix}{\mathrm{1}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{1}}\end{pmatrix} \\ $$$${find}\:{matrix}\:{B}\:{if}\: \\ $$$${BA}=\:{I} \\ $$$${find}\:{A}'\:{the}\:{reflection}\:{on}\:{the} \\ $$$${line}\:{y}\:=\:{x}\:{and}\:{A}''\:{the}\:{enlargement} \\ $$$${with}\:{matrix}\:\begin{pmatrix}{\mathrm{2}\:\:\:\:\:\:\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\:\:\mathrm{2}}\end{pmatrix}. \\ $$…

Question-39003

Question Number 39003 by behi83417@gmail.com last updated on 01/Jul/18 Answered by MJS last updated on 01/Jul/18 $${A}=\begin{pmatrix}{{a}}\\{\frac{\mathrm{1}}{{a}}}\end{pmatrix};\:{B}=\begin{pmatrix}{{b}}\\{\frac{\mathrm{1}}{{b}}}\end{pmatrix};\:{b}>{a} \\ $$$$\mid{AB}\mid=\frac{\left({b}−{a}\right)\sqrt{{a}^{\mathrm{2}} {b}^{\mathrm{2}} +\mathrm{1}}}{{ab}}={c} \\ $$$${M}_{{AB}} =\frac{{A}+{B}}{\mathrm{2}}=\begin{pmatrix}{\frac{{a}+{b}}{\mathrm{2}}}\\{\frac{{a}+{b}}{\mathrm{2}{ab}}}\end{pmatrix} \\…

a-line-with-equation-y-2x-5-the-point-1-7-lie-on-this-line-find-the-distance-between-this-line-and-the-line-joining-2-3-and-6-7-

Question Number 38996 by Rio Mike last updated on 01/Jul/18 $${a}\:{line}\:{with}\:{equation} \\ $$$$\:{y}\:=\:\mathrm{2}{x}\:+\:\mathrm{5}.{the}\:{point}\:\left(\mathrm{1},\mathrm{7}\right) \\ $$$${lie}\:{on}\:{this}\:{line}.{find}\:{the}\: \\ $$$${distance}\:{between}\:{this}\:{line}\: \\ $$$${and}\:{the}\:{line}\:{joining}\: \\ $$$$\left(\mathrm{2},\mathrm{3}\right)\:{and}\:\left(\mathrm{6},\mathrm{7}\right). \\ $$ Commented by…