Question

已知點(diǎn)M(3,5),在直線l:x-2y+2=0和y軸上各找一點(diǎn)P和Q,使△MPQ的周長(zhǎng)最小.

 

Answer 1

解析：如題圖,作點(diǎn)M關(guān)于直線l的對(duì)稱點(diǎn)M₁,再作點(diǎn)M關(guān)于y軸的對(duì)稱點(diǎn)M₂,連結(jié)M₁M₂與l及y軸交于P和Q兩點(diǎn),由軸對(duì)稱及平面幾何的知識(shí),可知這樣得到的△MPQ的周長(zhǎng)最小.?

由點(diǎn)M(3,5)及直線l,可求得點(diǎn)M關(guān)于直線l的對(duì)稱點(diǎn)M₁(5,1),同樣容易求得點(diǎn)M關(guān)于y軸的對(duì)稱點(diǎn)M₂(-3,5).?

據(jù)M₁和M₂兩點(diǎn)可得直線M₁M₂的方程為x+2y-7=0,?

令x=0,得直線M₁M₂和y軸的交點(diǎn)Q(0,).?