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Lesson: Parallelograms in the Coordinate Plane

In this lesson, we will learn how to use the distance, slope, and midpoint formulas to determine whether a quadrilateral in the coordinate plane is a parallelogram.

Question Video: Determining Whether a Given Quadrilateral Is a Parallelogram or Not given Its Vertices’ Coordinates Using the Distance Formula

03:39

Worksheet: Parallelograms in the Coordinate Plane • 11 Questions

Q1:

Consider quadrilateral with vertices , , , and . Using the distance formula, determine whether the quadrilateral is a parallelogram.

  • Ano
  • Byes

Q2:

Consider quadrilateral with vertices , , , and . Using the distance formula, determine whether the quadrilateral is a parallelogram.

  • Ayes
  • Bno

Q3:

The points , , , and are the vertices of quadrilateral . Using the slope formula, is the quadrilateral a parallelogram?

  • Ano
  • Byes

Q4:

The points , , , and are the vertices of quadrilateral . Using the slope formula, is the quadrilateral a parallelogram?

  • Ano
  • Byes

Q5:

If is a quadrilateral, , , , and , find the midpoint of and , then determine what type of figure is.

  • A , parallelogram
  • B , parallelogram
  • C , trapezoid
  • D , trapezoid

Q6:

If is a quadrilateral, , , , and , find the midpoint of and , then determine what type of figure is.

  • A , parallelogram
  • B , parallelogram
  • C , trapezoid
  • D , trapezoid

Q7:

Quadrilateral has vertices , , , and . Using the midpoint formula, determine whether is a parallelogram.

  • AIt is not a parallelogram.
  • BIt is a parallelogram.

Q8:

Quadrilateral has vertices , , , and . Using the midpoint formula, determine whether is a parallelogram.

  • AIt is a parallelogram.
  • BIt is not a parallelogram.

Q9:

Where must the coordinates of point be so that is a parallelogram? In that case, what is the area of the parallelogram?

  • A , area = 35
  • B , area = 24
  • C , area = 35
  • D , area = 24

Q10:

Where must the coordinates of point be so that is a parallelogram? In that case, what is the area of the parallelogram?

  • A , area = 36
  • B , area = 24
  • C , area = 36
  • D , area = 24

Q11:

Where must the coordinates of point be so that is a parallelogram? In that case, what is the area of the parallelogram?

  • A , area = 49
  • B , area = 28
  • C , area = 49
  • D , area = 28
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