Question

The coordinates of the vertices of parallelogram ABCD are A(-3,2) , B (-2,-1) , C ( 4,1) and D ( 3,4). The slopes of which line segments could be calculated to show that ABCD is a rectangle?

1) AB and DC
2) Ab and BC
3) AD and BC
4) AC and BD
When you say what answer you chose can you explain why that’s the answer please in depth?

Answer 1

The answer is Ab and BC, option 2
I cannot draw the rectangle here. When you draw the line of x and y axis, plot the numbers, when you connect the dot, you will see the rectangle.I don't know how to draw it here, but that is the answer.

Answer 2

NOTE:
To show that a parallelogram is a rectangle, we need to show that ONE of the interior angles is a right angle.
Therefore we need to find the angle between two adjacent sides.

To find two adjacent sides in a parallelogram with vertices in counter-clockwise, we need two sides with a common vertex, for example,
AB+BC, or BC+CD, or CD+DA, or DA+AB.

Any two sides without a common vertex are opposite sides.