Question

2) Quadrilateral ABCD has vertices A(-6,3), B(-3,6), C(9,6), and D(-5,-8). 1 V Using coordinate geometry, prove that (1) ABCD is a trapezoid (2) not an isosceles trapezoid

Answer 1

To prove that the points ABCD form a trapezoid, we must first plot the points on the cartesian (x,y) plane. The figure below is such a plot:

Now, one crucial property of any trapezoid is that it must have two opposites sides that are parallel to each other. The sketched plot above already gives us an idea of the sides that could be exactly parallel to each other, but the question asks that we carry out the proof using 'coordinate geometry'. Therefore, we have to apply our knowledge of coordinate geometry to carry out the proof.

According to coordinate geometry, two straight lines are said to be parallel to each other only if they have the sam