Worksheet: Parallelograms on the Coordinate Plane

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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
  • C−12,−5,−12,−5, parallelogram
  • D−12,−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:

Calculate, to two decimal places, the area of the parallelogram 𝑃𝑄𝑅𝑆, where the coordinates of its vertices are at 𝑃(2,1,3), 𝑄(1,4,5), 𝑅(2,5,3), and 𝑆(3,2,1).

Q11:

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

  • Ayes
  • Bno

Q12:

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(−1,4), area = 36
  • B(4,−1), area = 36
  • C(−1,4), area = 24
  • D(4,−1), area = 24

Q13:

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(−1,3), area = 48
  • B(3,−1), area = 48
  • C(−1,3), area = 28
  • D(3,−1), area = 28

Q14:

If 𝐴𝐵𝐶𝐷 is a quadrilateral, 𝐴=(−8,1), 𝐵=(8,4), 𝐶=(−2,8), and 𝐷=(−18,5), find the midpoint of 𝐴𝐶 and 𝐵𝐷, then determine what type of figure 𝐴𝐵𝐶𝐷 is.

  • A−10,92,−10,92, trapezoid
  • B0,−12,132,−7, parallelogram
  • C−5,92,−5,92, parallelogram
  • D(−5,9),(−5,9), trapezoid

Q15:

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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