3D geometry, what are the coordinates of the 4th vertex and the point of intersection of this trapezoid?












0














3 Vertex of the trapezoid are given : A(4,-1,2) B(7,1,-3) D(0,-4,6) and we know that AB and CD are parallel, and CD=2AB (opposite vertices are B-D and A-C)



The question is : what are the coordinates of vertex C, and what are the coordinates of the point of intersection of the diagonals?



Thank you!






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  • What have you tried?
    – YiFan
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3 Vertex of the trapezoid are given : A(4,-1,2) B(7,1,-3) D(0,-4,6) and we know that AB and CD are parallel, and CD=2AB (opposite vertices are B-D and A-C)



The question is : what are the coordinates of vertex C, and what are the coordinates of the point of intersection of the diagonals?



Thank you!






geometry 3d







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New contributor




20190104 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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  • What have you tried?
    – YiFan
    Jan 4 at 12:04














0












0








0







3 Vertex of the trapezoid are given : A(4,-1,2) B(7,1,-3) D(0,-4,6) and we know that AB and CD are parallel, and CD=2AB (opposite vertices are B-D and A-C)



The question is : what are the coordinates of vertex C, and what are the coordinates of the point of intersection of the diagonals?



Thank you!






geometry 3d







share|cite|improve this question









New contributor




20190104 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











3 Vertex of the trapezoid are given : A(4,-1,2) B(7,1,-3) D(0,-4,6) and we know that AB and CD are parallel, and CD=2AB (opposite vertices are B-D and A-C)



The question is : what are the coordinates of vertex C, and what are the coordinates of the point of intersection of the diagonals?



Thank you!






geometry 3d




geometry 3d






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share|cite|improve this question









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edited Jan 4 at 11:54







20190104













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asked Jan 4 at 11:43









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  • What have you tried?
    – YiFan
    Jan 4 at 12:04


















  • What have you tried?
    – YiFan
    Jan 4 at 12:04
















What have you tried?
– YiFan
Jan 4 at 12:04




What have you tried?
– YiFan
Jan 4 at 12:04










2 Answers
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Hint: From parallelism, $vec{AB} = kvec{CD}$ for some negative $k$. Find $k$; so $1/k(B-A) + D = C$. To get the intersection of the diagonals, look at the lines $t(C - A)$ and $r(D-B)$ and their intersection.






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    0














    Let $$C[x_C,y_C,z_c]$$ then $$2[0-x_C,-4-y_C,6-z_C]=[7-4,1+1,-3-2]$$ Can you solve this?
    You will get $$-2x_C=3,-8-2y_C=2,12-2z_C=-5$$






    share|cite|improve this answer























    • Thank you, and from the 4 vertices how can i get the point of intersection of the diagonals?
      – 20190104
      Jan 4 at 12:20












    • Should i post you the solution?
      – Dr. Sonnhard Graubner
      Jan 4 at 12:21










    • i would appreciate that!
      – 20190104
      Jan 4 at 12:23










    • I got (14/3, -2/3, 0) for the intersection point. Is it right?
      – 20190104
      Jan 4 at 15:13













    Your Answer





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    2 Answers
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    0














    Hint: From parallelism, $vec{AB} = kvec{CD}$ for some negative $k$. Find $k$; so $1/k(B-A) + D = C$. To get the intersection of the diagonals, look at the lines $t(C - A)$ and $r(D-B)$ and their intersection.






    share|cite|improve this answer




























      0














      Hint: From parallelism, $vec{AB} = kvec{CD}$ for some negative $k$. Find $k$; so $1/k(B-A) + D = C$. To get the intersection of the diagonals, look at the lines $t(C - A)$ and $r(D-B)$ and their intersection.






      share|cite|improve this answer


























        0












        0








        0






        Hint: From parallelism, $vec{AB} = kvec{CD}$ for some negative $k$. Find $k$; so $1/k(B-A) + D = C$. To get the intersection of the diagonals, look at the lines $t(C - A)$ and $r(D-B)$ and their intersection.






        share|cite|improve this answer














        Hint: From parallelism, $vec{AB} = kvec{CD}$ for some negative $k$. Find $k$; so $1/k(B-A) + D = C$. To get the intersection of the diagonals, look at the lines $t(C - A)$ and $r(D-B)$ and their intersection.







        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited Jan 4 at 12:15

























        answered Jan 4 at 12:00









        Lucas HenriqueLucas Henrique

        968414




        968414























            0














            Let $$C[x_C,y_C,z_c]$$ then $$2[0-x_C,-4-y_C,6-z_C]=[7-4,1+1,-3-2]$$ Can you solve this?
            You will get $$-2x_C=3,-8-2y_C=2,12-2z_C=-5$$






            share|cite|improve this answer























            • Thank you, and from the 4 vertices how can i get the point of intersection of the diagonals?
              – 20190104
              Jan 4 at 12:20












            • Should i post you the solution?
              – Dr. Sonnhard Graubner
              Jan 4 at 12:21










            • i would appreciate that!
              – 20190104
              Jan 4 at 12:23










            • I got (14/3, -2/3, 0) for the intersection point. Is it right?
              – 20190104
              Jan 4 at 15:13


















            0














            Let $$C[x_C,y_C,z_c]$$ then $$2[0-x_C,-4-y_C,6-z_C]=[7-4,1+1,-3-2]$$ Can you solve this?
            You will get $$-2x_C=3,-8-2y_C=2,12-2z_C=-5$$






            share|cite|improve this answer























            • Thank you, and from the 4 vertices how can i get the point of intersection of the diagonals?
              – 20190104
              Jan 4 at 12:20












            • Should i post you the solution?
              – Dr. Sonnhard Graubner
              Jan 4 at 12:21










            • i would appreciate that!
              – 20190104
              Jan 4 at 12:23










            • I got (14/3, -2/3, 0) for the intersection point. Is it right?
              – 20190104
              Jan 4 at 15:13
















            0












            0








            0






            Let $$C[x_C,y_C,z_c]$$ then $$2[0-x_C,-4-y_C,6-z_C]=[7-4,1+1,-3-2]$$ Can you solve this?
            You will get $$-2x_C=3,-8-2y_C=2,12-2z_C=-5$$






            share|cite|improve this answer














            Let $$C[x_C,y_C,z_c]$$ then $$2[0-x_C,-4-y_C,6-z_C]=[7-4,1+1,-3-2]$$ Can you solve this?
            You will get $$-2x_C=3,-8-2y_C=2,12-2z_C=-5$$







            share|cite|improve this answer














            share|cite|improve this answer



            share|cite|improve this answer








            edited Jan 4 at 12:54

























            answered Jan 4 at 12:02









            Dr. Sonnhard GraubnerDr. Sonnhard Graubner

            73.5k42865




            73.5k42865












            • Thank you, and from the 4 vertices how can i get the point of intersection of the diagonals?
              – 20190104
              Jan 4 at 12:20












            • Should i post you the solution?
              – Dr. Sonnhard Graubner
              Jan 4 at 12:21










            • i would appreciate that!
              – 20190104
              Jan 4 at 12:23










            • I got (14/3, -2/3, 0) for the intersection point. Is it right?
              – 20190104
              Jan 4 at 15:13




















            • Thank you, and from the 4 vertices how can i get the point of intersection of the diagonals?
              – 20190104
              Jan 4 at 12:20












            • Should i post you the solution?
              – Dr. Sonnhard Graubner
              Jan 4 at 12:21










            • i would appreciate that!
              – 20190104
              Jan 4 at 12:23










            • I got (14/3, -2/3, 0) for the intersection point. Is it right?
              – 20190104
              Jan 4 at 15:13


















            Thank you, and from the 4 vertices how can i get the point of intersection of the diagonals?
            – 20190104
            Jan 4 at 12:20






            Thank you, and from the 4 vertices how can i get the point of intersection of the diagonals?
            – 20190104
            Jan 4 at 12:20














            Should i post you the solution?
            – Dr. Sonnhard Graubner
            Jan 4 at 12:21




            Should i post you the solution?
            – Dr. Sonnhard Graubner
            Jan 4 at 12:21












            i would appreciate that!
            – 20190104
            Jan 4 at 12:23




            i would appreciate that!
            – 20190104
            Jan 4 at 12:23












            I got (14/3, -2/3, 0) for the intersection point. Is it right?
            – 20190104
            Jan 4 at 15:13






            I got (14/3, -2/3, 0) for the intersection point. Is it right?
            – 20190104
            Jan 4 at 15:13












            20190104 is a new contributor. Be nice, and check out our Code of Conduct.










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