VIII - Geometric Vectors - SLC Home Page
VIII - Geometric Vectors - SLC Home Page
VIII - Geometric Vectors - SLC Home Page
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Math NYC<strong>VIII</strong> – <strong>Geometric</strong> <strong>Vectors</strong>11. We need to show that AB DC and BC AD .ForForAB DC , we have OB OA OC ODOB AO OC DOAO OB DO OCAB DCBC AD we have OB OA OC ODOD OA OC OBOD AO OC BOAO OD BO OCAD BC12. We need to show that PQRS is a parallelogram whose sides have equal length.BPAPQ PA AS SR RC CQ PA BQ SR AP QB AP QB SR AP QB SRQSSince ABCD is a rectangle and P,Q,R and S aremidpoints, thenAP PB DR RCAS SD BQ QCQR QP PS SR PQ PS SR SR PS SR PSTo show that all sides are of equal length, it suffices to show that PQproved that PQRS is a parallelogram.2 2 2PQ PB BQCRD(by the Pythagorean theorem) PS since we haveAP2 2ASPS2(by the Pythagorean theorem)hence PQPSFall 2012 Martin Huard 5
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