10th Class
Mathematics
Coordinate Geometry
Question Bank
Coordinate Geometry
question_answer
Points \[(6,\,8),\,(3,7),(-2,-2)\] and \[(1,-1)\] are joined to form a quadrilateral. What will be the structure of quadrilateral?
A)Rhombus
B) Parallelogram
C) Square
D) Rectangle
Correct Answer:
B
Solution :
Let the points be \[A(6,8),\,\,B(3,\,7),\,\,C(-2,-2)\]And \[D(1,-1)\] Now, \[AB=\sqrt{{{(3-6)}^{2}}+{{(7-8)}^{2}}}=\sqrt{10}\] \[BC=\sqrt{{{(-2-3)}^{2}}+{{(-2-7)}^{2}}}=\sqrt{106}\] \[CD=\sqrt{{{(1+2)}^{2}}+{{(-1+2)}^{2}}}=\sqrt{10}\] \[DA=\sqrt{{{(6-1)}^{2}}+{{(8+1)}^{2}}}=\sqrt{106}\] Also\[AC=\sqrt{{{(8)}^{2}}+{{(10)}^{2}}}=\sqrt{64+100}=\sqrt{164}\] \[BD=\sqrt{{{(2)}^{2}}+{{(8)}^{2}}}=\sqrt{4+64}=\sqrt{68}\] Since, \[AB=DC\]and \[BC=DA\]and\[AC\ne BD.\]. \[\therefore \] It is a parallelogram.