Worksheet: Parallelograms on the Coordinate Plane

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

  • Ayes
  • Bno

Q2:

If 𝐴𝐡𝐢𝐷 is a quadrilateral, 𝐴=(βˆ’2,βˆ’17), 𝐡=(βˆ’14,10), 𝐢=(1,7), and 𝐷=(13,βˆ’20), find the midpoint of 𝐴𝐢 and 𝐡𝐷, then determine what type of figure 𝐴𝐡𝐢𝐷 is.

  • A(βˆ’1,βˆ’5),(βˆ’1,βˆ’5), trapezoid
  • Bο€Ό52,βˆ’8,ο€Όβˆ’17,232, parallelogram
  • Cο€Όβˆ’12,βˆ’5,ο€Όβˆ’12,βˆ’5, parallelogram
  • Dο€Όβˆ’12,βˆ’10,ο€Όβˆ’12,βˆ’10, trapezoid

Q3:

Where must the coordinates of point 𝐢 be so that 𝐴𝐡𝐢𝐷 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 𝐴𝐡𝐢𝐷 is a parallelogram, what can be said of the slope of line ⃖⃗𝐴𝐡?

  • Athe slope of line ⃖⃗𝐴𝐡 = the slope of line ⃖⃗𝐴𝐢
  • Bthe slope of line ⃖⃗𝐴𝐡 = the slope of line ⃖⃗𝐴𝐷
  • Cthe slope of line ⃖⃗𝐴𝐡 = the slope of line ⃖⃗𝐡𝐢
  • Dthe slope of line ⃖⃗𝐴𝐡 = the slope of line ⃖⃗𝐢𝐷

Q5:

𝐴𝐡𝐢𝐷 is a parallelogram. The coordinates of the points 𝐴, 𝐡, and 𝐢 are (0,βˆ’2), (4,7), and (6,3) respectively. Find the coordinates of 𝐷.

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

Q6:

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

Q7:

Given that 𝐿=(βˆ’5,βˆ’6,0), 𝑀=(βˆ’2,βˆ’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, 𝐡, 𝐢, and 𝐷 with coordinates (βˆ’1,1), (1,3), (3,βˆ’1), and (1,βˆ’3) respectively.

Work out the perimeter of the parallelogram 𝐴𝐡𝐢𝐷. 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 𝐴𝐡𝐢𝐷.

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(βˆ’5,1), 𝐿(1,0), 𝑀(3,βˆ’2), and 𝑁(βˆ’3,βˆ’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 𝐢 be so that 𝐴𝐡𝐢𝐷 is a parallelogram? In that case, what is the area of the parallelogram?

  • A(βˆ’1,4), area = 36
  • B(4,βˆ’1), area = 36
  • C(βˆ’1,4), area = 24
  • D(4,βˆ’1), area = 24

Q13:

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

  • A(βˆ’1,3), area = 48
  • B(3,βˆ’1), area = 48
  • C(βˆ’1,3), area = 28
  • D(3,βˆ’1), area = 28

Q14:

If 𝐴𝐡𝐢𝐷 is a quadrilateral, 𝐴=(βˆ’8,1), 𝐡=(8,4), 𝐢=(βˆ’2,8), and 𝐷=(βˆ’18,5), find the midpoint of 𝐴𝐢 and 𝐡𝐷, then determine what type of figure 𝐴𝐡𝐢𝐷 is.

  • Aο€Όβˆ’10,92,ο€Όβˆ’10,92, trapezoid
  • Bο€Ό0,βˆ’12,ο€Ό132,βˆ’7, parallelogram
  • Cο€Όβˆ’5,92,ο€Όβˆ’5,92, parallelogram
  • D(βˆ’5,9),(βˆ’5,9), trapezoid

Q15:

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

  • ARhombus
  • BParallelogram
  • CSquare
  • DRectangle
  • ETrapezoid

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