Dalam segi empat , diketahui titik-titik sudut , , , , , , dan , . Titik-titik P, Q, R, dan S berturut-turut adalah titik-titik tengah , , , , , , dan , ., a.Perlihatkan bahwa segi empat , adalah bangun geometri persegi panjang.

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PERTANYAAN :


Dalam segi empat ABCD diketahui titik-titik sudut straight A left parenthesis 2 comma space minus space 1 comma space 0 right parenthesis, straight B left parenthesis 0 comma space minus 1 comma space minus 1 right parenthesis, straight C left parenthesis 1 comma space 1 comma space minus 3 right parenthesis, dan straight D left parenthesis 3 comma space 1 comma space minus 2 right parenthesis. Titik-titik P, Q, R, dan S berturut-turut adalah titik-titik tengah AB, BC, CD, dan DA.

Baca Juga :  Dari angka-angka 0, 1, 2, 3, 4, 5, dan 6 akan dibentuk bilangan ribuan. Tentukan:, a. banyak bilangan ribuan yang dapat dibentuk.

a. Perlihatkan bahwa segi empat ABCD adalah bangun geometri persegi panjang.

Jawaban

 segi empat ABCD adalah bangun geometri persegi panjang.


Pembahasan

Jawaban yang benar untuk pertanyaan tersebut segi empat bold ABCD adalah bangun geometri persegi panjang.

Ingat!

  • Persegi panjang adalah bangun datar yang dibentuk oleh dua pasang sisi yang masing-masing sama panjang dan sejajar dengan pasangannya, dan memiliki empat buah sudut yang kesemuanya adalah sudut siku-siku.
  • Rumus sudut antar dua vektor : 

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space theta end cell equals cell fraction numerator AB with rightwards arrow on top times BC with rightwards arrow on top over denominator open vertical bar AB with rightwards arrow on top close vertical bar open vertical bar BC with rightwards arrow on top close vertical bar end fraction end cell end table 

Dalam segi empat ABCD diketahui titik-titik sudut straight A left parenthesis 2 comma space minus space 1 comma space 0 right parenthesis, straight B left parenthesis 0 comma space minus 1 comma space minus 1 right parenthesis, straight C left parenthesis 1 comma space 1 comma space minus 3 right parenthesis, dan straight D left parenthesis 3 comma space 1 comma space minus 2 right parenthesis, oleh karena itu:

  • Pada Vektor:
Baca Juga :  , Afgan has always been my favorite singer. I had always been thinking of how I would feel when I met him. Then I was suddenly hit by lightning when I found out Afgan was coming to town for a concert in a local auditorium. A day before the concert, there would be a meet-and-greet event at a local radio station. Feeling excited, I packed all my Afgan’s CDs to get his signature at the event., On that bright and sunny Saturday morning, the radio station was full of Afganism (that’s how Afgan’s fans are called). They sat on the chairs prepared inside the radio station’s lobby. Some stood in rows in the front yard of the radio station. A spot inside a lobby was prepared with a mini stage for Afgan’s singing performance and a table for Afgan to sign Afganism’s memorabilia. Finally, after about 40 or 50 minutes wait, Afgan showed up from inside the radio station. He smiled and waved to all Afganism who had been waiting excitedly saying, “Good morning. How are you all?” The crowd went crazy. The shouts sounded like a mix of “Fine, thank you” and screams of Afgan’s name., Then, he started the event by singing his hit single “Dia dia dia”. Afganism went even crazier; they sang along with him throughout the song. Of course, I did too. I couldn’t take my eyes off this amazing singer who had released three albums. When he was finished with the song, the host announced that it was time for autographing the memorabilia. I prepared my CDs and began to stand in the line. When I arrived at the table, I was speechless. It was unreal just seeing him that close. I thought it was really cool seeing him like that because he really just felt like a normal person, which was awesome. He asked my name so that he could write it on the CD to say “To Mia, Love Afgan”. He was also very friendly, so I didn’t feel too nervous when I had a chance to take pictures with him. He was just an amazing person. That was one of the best days in my personal life history.

table attributes columnalign right center left columnspacing 0px end attributes row cell AB with rightwards arrow on top end cell equals cell b with rightwards arrow on top minus a with rightwards arrow on top end cell end table 

Dalam segi empat ABCD diketahui titik-titik sudut straight A left parenthesis 2 comma space minus space 1 comma space 0 right parenthesis, straight B left parenthesis 0 comma space minus 1 comma space minus 1 right parenthesis, straight C left parenthesis 1 comma space 1 comma space minus 3 right parenthesis, dan straight D left parenthesis 3 comma space 1 comma space minus 2 right parenthesis. Oleh karena itu:

table attributes columnalign right center left columnspacing 0px end attributes row cell AB with rightwards arrow on top end cell equals cell b with rightwards arrow on top minus a with rightwards arrow on top end cell row blank equals cell left parenthesis 0 comma space minus 1 comma space minus 1 right parenthesis minus left parenthesis 2 comma space minus 1 comma space 0 right parenthesis end cell row blank equals cell left parenthesis negative 2 comma space 0 comma space minus 1 right parenthesis end cell row blank blank blank row cell BC with rightwards arrow on top end cell equals cell c with rightwards arrow on top minus b with rightwards arrow on top end cell row blank equals cell left parenthesis 1 comma space 1 comma space minus 3 right parenthesis minus left parenthesis 0 comma space minus 1 comma space minus 1 right parenthesis end cell row blank equals cell left parenthesis 1 comma space 2 comma space minus 2 right parenthesis end cell row blank blank blank row cell DC with rightwards arrow on top end cell equals cell c with rightwards arrow on top minus d with rightwards arrow on top end cell row blank equals cell left parenthesis 1 comma space 1 comma space minus 3 right parenthesis minus left parenthesis 3 comma space 1 comma space minus 2 right parenthesis end cell row blank equals cell left parenthesis negative 2 comma space 0 comma space minus 1 right parenthesis end cell row blank blank blank row cell AD with rightwards arrow on top end cell equals cell d with rightwards arrow on top minus a with rightwards arrow on top end cell row blank equals cell left parenthesis 3 comma space 1 comma space minus 2 right parenthesis minus left parenthesis 2 comma space minus 1 comma space 0 right parenthesis end cell row blank equals cell left parenthesis 1 comma space 2 comma space minus 2 right parenthesis end cell end table  

Kita hitung sudut antara AB with rightwards arrow on top dan BC with rightwards arrow on top dengan melakukan perhitungan sebagai berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space theta end cell equals cell fraction numerator AB with rightwards arrow on top times BC with rightwards arrow on top over denominator open vertical bar AB with rightwards arrow on top close vertical bar open vertical bar BC with rightwards arrow on top close vertical bar end fraction end cell row blank equals cell fraction numerator left parenthesis negative 2 right parenthesis left parenthesis 1 right parenthesis plus left parenthesis 0 right parenthesis left parenthesis 2 right parenthesis plus left parenthesis negative 1 right parenthesis left parenthesis negative 2 right parenthesis over denominator square root of left parenthesis negative 2 right parenthesis squared plus 0 squared plus left parenthesis negative 1 right parenthesis squared end root square root of 1 squared plus 2 squared plus left parenthesis negative 2 right parenthesis squared end root end fraction end cell row blank equals cell fraction numerator negative 2 plus 0 plus 2 over denominator square root of 4 plus 0 plus 1 end root square root of 1 plus 4 plus 4 end root end fraction end cell row blank equals 0 row blank blank blank row theta equals cell 90 degree end cell end table  

Pada segiempat ABCD terlihat dua pasang sisinya sama sejajar dan sama panjang yaitu AB with rightwards arrow on top equals DC with rightwards arrow on top dan BC with rightwards arrow on top equals AD with rightwards arrow on top dan sudut antara sudut antar sisi yang berdekatannya siku-siku.

Dengan demikian, segi empat ABCD adalah bangun geometri persegi panjang.


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