Lesson Worksheet: Parallelograms on the Coordinate Plane Mathematics • 11th Grade

In this worksheet, we will practice using the distance, slope, and midpoint formulas to determine whether a quadrilateral in the coordinate plane is a parallelogram.

Q1:

The points 𝐾(5,0), 𝐿(3,1), 𝑀(2,5), and 𝑁(4,6) are the vertices of quadrilateral 𝐾𝐿𝑀𝑁. Using the slope formula, is the quadrilateral a parallelogram?

  • AYes
  • BNo

Q2:

If 𝐴𝐵𝐶𝐷 is a quadrilateral, 𝐴=(2,17), 𝐵=(14,10), 𝐶=(1,7), and 𝐷=(13,20), find the midpoint of 𝐴𝐶 and 𝐵𝐷, then determine what type of figure 𝐴𝐵𝐶𝐷 is.

  • A(1,5),(1,5), trapezoid
  • B52,8,17,232, parallelogram
  • C12,5,12,5, parallelogram
  • D12,10,12,10, trapezoid

Q3:

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

  • A(6,5), area = 35
  • B(5,6), area = 35
  • C(6,5), area = 24
  • D(5,6), area = 24

Q4:

If 𝐴𝐵𝐶𝐷 is a parallelogram, what can be said of the slope of line 𝐴𝐵?

  • Athe slope of line 𝐴𝐵 = the slope of line 𝐴𝐶
  • Bthe slope of line 𝐴𝐵 = the slope of line 𝐴𝐷
  • Cthe slope of line 𝐴𝐵 = the slope of line 𝐵𝐶
  • Dthe slope of line 𝐴𝐵 = the slope of line 𝐶𝐷

Q5:

𝐴𝐵𝐶𝐷 is a parallelogram. The coordinates of the points 𝐴, 𝐵, and 𝐶 are (0,2), (4,7), and (6,3) respectively. Find the coordinates of 𝐷.

  • A(2,6)
  • B(10,6)
  • C(10,8)
  • D(2,8)

Q6:

Suppose that A=3,9,9 and B=8,7,5 fix two sides of a parallelogram. What is the area of this parallelogram, to the nearest hundredth?

Q7:

Given that 𝐿=(5,6,0), 𝑀=(2,7,8), and 𝑁=(2,6,4), determine the area of the parallelogram 𝐿𝑀𝑁𝐸 to the nearest hundredth.

Q8:

Determine, in square units, the area of the shown parallelogram.

Q9:

A parallelogram has vertices at the points 𝐴, 𝐵, 𝐶, and 𝐷 with coordinates (1,1), (1,3), (3,1), and (1,3) respectively.

Work out the perimeter of the parallelogram 𝐴𝐵𝐶𝐷. Give your solution to one decimal place.

By drawing a rectangle through the vertices of the parallelogram, or otherwise. Work out the area of the parallelogram 𝐴𝐵𝐶𝐷.

Q10:

A quadrilateral has vertices at the points (2,1),(3,3),(6,1), and (5,1). What is the name of the quadrilateral?

  • ARhombus
  • BParallelogram
  • CSquare
  • DRectangle
  • ETrapezoid

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