Question

James states that quadrilateral

formed by A (-1, -3), B (5, 1), C (9, 0),
and D (3,-4) is a parallelogram. Using mathematics, prove that the quadrilateral is a parallelogram

Answer 1

Using the distance formula,

`AD=\sqrt{(-1-3)^(2)+(-3-(-4))^(2)}=√(17)\\\\BC=\sqrt{(5-9)^(2)+(1-0)^(2)}=√(17) \\\\\therefore \overline{AD} \cong \overline{BC}`

`AB=\sqrt{(-1-5)^(2)+(-3-1)^(2)}=√(52)=2√(13)\\\\CD=\sqrt{(9-3)^(2)+(0-(-4))^(2)}=√(52)=2√(13)\\\\\therefore \overline{AB} \cong \overline{CD}`

Since ABCD has two pairs of opposite congruent sides, it is a parallelogram.