Question

The vertices of quadrilateral ABCD are A(3,0), B(4,3), C(7,3), D(6,0).

Answer 1

(a) If AB = CD and AB || CD then ABCD is a parallelogram.

$A(3,0), B(4,3), C(7,3), D(6,0) \\d(A,B)= \sqrt{(4-3)^2+(3-0)^2} = \sqrt{10} \\d(C,D)= \sqrt{(6-7)^2+(0-3)^2} = \sqrt{10} \\AB=CD \\ \\m_{AB}= \frac{3-0}{4-3} = \\ \\m_{CD}= \frac{0-3}{6-7}=3 \\ \\m_{AB}=m_{CD}\Rightarrow AB||CD$

(b) If AB ≠ BC then ABCD is not a rhombus.

$B(4,3), C(7,3) \\d(B,C)= \sqrt{(7-4)^2+(3-3)^2}=3 \\BC \neq AB$