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(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 ) , trapezium
  • B 5 2 , 8 , 1 7 , 2 3 2 , parallelogram
  • C 1 2 , 5 , 1 2 , 5 , parallelogram
  • D 1 2 , 1 0 , 1 2 , 1 0 , trapezium

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:

𝐴 𝐵 𝐶 𝐷 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 ( 1 0 , 6 )
  • C ( 1 0 , 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 1 0 , 9 2 , 1 0 , 9 2 , trapezium
  • B 0 , 1 2 , 1 3 2 , 7 , parallelogram
  • C 5 , 9 2 , 5 , 9 2 , parallelogram
  • D ( 5 , 9 ) , ( 5 , 9 ) , trapezium

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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