Question

show the diagonals of the quadrilateral formed by the vertices (-1,2).(5,4),(3,4) and ,(-3,2) taken in order bisect each other​

Answer 1

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Answer 2

To show that the diagonals of the quadrilateral formed by the given vertices bisect each other.

• Let the vertices be

                    A(-1, 2)

                    B(5, 4)

                    C(3, 4)

                    D(-3, 2)

• AC and BD are diagonals.

• To prove diagonals bisect each other, we need to prove

                 Midpoint of AC = Midpoint of BD

                  $(\frac{x_{1}+x_{3} }{2},\frac{y_{1}+y_{3} }{2})=(\frac{x_{2}+x_{4} }{2},\frac{y_{2}+y_{4} }{2})$

                   $(\frac{-1+3 }{2},\frac{2+4 }{2})=(\frac{5-3}{2},\frac{4+2}{2})$

                    $(\frac{2}{2},\frac{6}{2})=(\frac{2}{2},\frac{6}{2})$

                     (1, 3) = (1, 3)

∴ The diagonals of the quadrilateral formed by the given vertices taken in order bisect each other.