Question

If A(6, 1), B(8, 2), C(9, 4) and D(7, 3) are the vertices of a closed figure ABCD, then ABCD is a _______.

• A. Cube
• B. Trapezium
• C. Triangle
• D. Parallelogram

Answer 1

The correct option is D Parallelogram

Given, A(6, 1), B(8, 2), C(9, 4) and D(7, 3)

Slope of a line = $\frac{y_2-y_1}{x_2-x_1}$

Slope of line AB = $\frac{2-1}{8-6}=\frac{1}{2}$
Slope of line BC = $\frac{4-2}{9-8}=2$
Slope of line CD = $\frac{3-4}{7-9}=\frac{-1}{-2}=\frac{1}{2}$
Slope of line DA = $\frac{3-1}{7-6}=2$

Slope of line AB = Slope of line CD
Slope of line BC = Slope of line DA

$\therefore$ BC || DA & AB || CD

Both the pairs of opposite sides of the quadrilateral are parallel.
$\therefore$ ABCD is a parallelogram.