英语周报八年级下册第52期答案

第三节One possible versionParagraph 1Finally, afler struggling for a minute or tuo, I still gotpulled underwater. I told myself I should never give upThen I pulled the weed again with great efforts. The weedfinally broke. I swam back to the surface to take a debreath. I saw two young men in canoes, racing each other.I was exhausted and shouted for help. The two men saw meand raced towards me. By the time they reached me, I hadbeen already unconsciousParagraph 2When woke up, I was in an empty room lying on abed. It was not until a doctor came into the room that I realized that I was in a hospital. Jimmy and Bobby told me thetwo young men brought me to the shore and sent me to thehospital. After a few minutes, my parents with half angryand half worried faces walked in. My parents scolded me ifor running out of the house secretly but were also glad thatI was not seriously injured. I will never forget that terrifyingexperience. Neither will I ever want to show off again

16.4【解析】在△ABC中,设O为BC中点,由正三角形性质可知,AO⊥BC,以O为原点,BC为x轴,AO为y轴,平面BCC1B1中过点O且垂直于BC的直线为z轴,建立空间直角坐标系,如图所示,因为点P是侧面BCC1B1内的动点,且A1P∥平面BCM,则P点的轨迹是过A:点与平面MBC平行的平面与侧面BCC1B1的交线,则P点的轨迹是连接侧棱BB1,CC1中点的线段l1,因为Q是底面ABC内的动点,且PQ⊥平面BCM,则有PQ⊥MB,PQ⊥MC.因为正三棱锥的棱长均为2,点M是侧棱AA1的中点,所以M(0,-√3,1),B(1,0,0),C(-1,0,0).设P(x:1,0,1),Q(x2,y,0),故MB=(1,3,1),MC=(-1,3,-1),PQ=(x2-x1,y,-1),MB·PQ=0,(x2-x1)+3y+1=0,而即解MC·PQ=0(x2-x1)+√3y+1=0,得y=x1=x2.因为点P的轨迹是连接侧棱BB1,CC1中点的线段l1,其中l1∥BC,且x1=x2,所以点Q的轨迹l2∥BC,所以根据相似可知点Q的/33轨迹长为×2√3MA

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