Question

7 a fish farm builds a breeding basin in the form of a quadrilateral abcd, with a(-3, -1), b(2, 0), c(5, 3) and d(0, 2). show that the quadrilateral abcd is a parallelogram.

Explanation:

Step1: Calculate slope of AB

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m_{AB}=\frac{0-(-1)}{2-(-3)}=\frac{1}{5}$

Step2: Calculate slope of CD

$m_{CD}=\frac{2-3}{0-5}=\frac{-1}{-5}=\frac{1}{5}$

Step3: Calculate slope of BC

$m_{BC}=\frac{3-0}{5-2}=\frac{3}{3}=1$

Step4: Calculate slope of DA

$m_{DA}=\frac{-1-2}{-3-0}=\frac{-3}{-3}=1$

Step5: Verify parallel sides

Parallel lines have equal slopes: $m_{AB}=m_{CD}$, $m_{BC}=m_{DA}$

Answer:

Since opposite sides of quadrilateral ABCD have equal slopes (are parallel), ABCD is a parallelogram.