Diketahui titik A(5,-3), B(-2,-7), dan C(-6,1). Tentukan  AB+(BC+AC)!

Pertanyaan

Diketahui titik A(5,-3), B(-2,-7), dan C(-6,1). Tentukan  begin mathsize 14px style AB with rightwards arrow on top plus open parentheses BC with rightwards arrow on top plus stack A C with rightwards arrow on top close parentheses end style!

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

 begin mathsize 14px style AB with rightwards arrow on top plus open parentheses BC with rightwards arrow on top plus stack A C with rightwards arrow on top close parentheses end style  = begin mathsize 14px style open parentheses negative 22 comma 8 close parentheses end style 

Pembahasan

vektor posisi dari titik A, B, dan C masing-masing sebagai berikut.

stack size 14px O size 14px A with size 14px rightwards arrow on top size 14px equals size 14px a with size 14px rightwards arrow on top size 14px equals begin mathsize 14px style left parenthesis 5 comma negative 3 right parenthesis end style stack size 14px O size 14px B with size 14px rightwards arrow on top size 14px equals size 14px b with size 14px rightwards arrow on top size 14px equals begin mathsize 14px style left parenthesis negative 2 comma negative 7 right parenthesis end style size 14px space stack size 14px O size 14px C with size 14px rightwards arrow on top size 14px equals size 14px c with size 14px rightwards arrow on top size 14px equals begin mathsize 14px style left parenthesis negative 6 comma 1 right parenthesis end style 

Diperoleh  begin mathsize 14px style AB with rightwards arrow on top comma space BC with rightwards arrow on top comma space end styledan begin mathsize 14px style AC with rightwards arrow on top end style

begin mathsize 14px style AB with rightwards arrow on top equals b with rightwards arrow on top minus a with rightwards arrow on top space space space space space space equals left parenthesis negative 2 comma negative 7 right parenthesis minus left parenthesis 5 comma negative 3 right parenthesis space space space space space space equals left parenthesis negative 2 minus 5 comma negative 7 plus 3 right parenthesis space space space space space space equals left parenthesis negative 7 comma negative 4 right parenthesis BC with rightwards arrow on top equals c with rightwards arrow on top minus b with rightwards arrow on top space space space space space space equals left parenthesis negative 6 comma 1 right parenthesis minus left parenthesis negative 2 comma negative 7 right parenthesis space space space space space space equals left parenthesis negative 6 plus 2 comma 1 plus 7 right parenthesis space space space space space space equals left parenthesis negative 4 comma 8 right parenthesis stack A C with rightwards arrow on top equals c with rightwards arrow on top minus a with rightwards arrow on top space space space space space equals open parentheses negative 6 comma 1 close parentheses minus open parentheses 5 comma negative 3 close parentheses space space space space space equals open parentheses negative 6 minus 5 comma 1 plus 3 close parentheses space space space space space equals open parentheses negative 11 comma 4 close parentheses end style  

Selanjutnya akan ditentukan  begin mathsize 14px style AB with rightwards arrow on top plus open parentheses BC with rightwards arrow on top plus stack A C with rightwards arrow on top close parentheses end style

begin mathsize 14px style stack B C with rightwards arrow on top plus stack A C with rightwards arrow on top equals left parenthesis negative 4 comma 8 right parenthesis plus left parenthesis negative 11 comma 4 right parenthesis space space space space space space space space space space space space space space space equals left parenthesis negative 4 minus 11 comma 4 plus 8 right parenthesis space space space space space space space space space space space space space space space equals left parenthesis negative 15 comma 12 right parenthesis stack A B with rightwards arrow on top plus left parenthesis stack B C with rightwards arrow on top plus stack A C with rightwards arrow on top right parenthesis equals left parenthesis negative 7 comma negative 4 right parenthesis plus left parenthesis negative 15 comma 12 right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space equals open parentheses negative 7 minus 15 comma negative 4 plus 12 close parentheses space space space space space space space space space space space space space space space space space space space space space space space space equals left parenthesis negative 22 comma 8 right parenthesis end style  

Jadi, begin mathsize 14px style AB with rightwards arrow on top plus open parentheses BC with rightwards arrow on top plus stack A C with rightwards arrow on top close parentheses end style  = begin mathsize 14px style open parentheses negative 22 comma 8 close parentheses end style 

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