Parallelograms in the Coordinate Plane

Front

What is a parallelogram?

Back

A parallelogram is a four-sided figure (quadrilateral) with opposite sides that are parallel and equal in length.

Front

How can you find the coordinates of the fourth vertex of a parallelogram given three vertices?

Back

Use the midpoint formula: If J, K, and L are three vertices, then M can be found using the equation M = J + K - L.

Front

What is the slope of a line segment between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

If two sides of a parallelogram have different slopes, what can be concluded about the shape?

Back

If the slopes are different, the shape is just a parallelogram and not a rectangle or square.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

What properties do the opposite sides of a parallelogram have?

Back

The opposite sides of a parallelogram are equal in length and parallel.

Front

What is the relationship between the slopes of opposite sides in a parallelogram?

Back

The slopes of opposite sides are equal.

Front

How can you determine if a quadrilateral is a parallelogram using side lengths?

Back

If both pairs of opposite sides are equal in length, the quadrilateral is a parallelogram.

Front

What is the significance of the diagonals in a parallelogram?

Back

The diagonals of a parallelogram bisect each other.