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Worksheet: Parallelograms in 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 𝐾 𝐿 𝑀 𝑁 . Using the slope formula, is the quadrilateral a parallelogram?

  • Ayes
  • Bno

Q2:

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

  • Ayes
  • Bno

Q3:

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

Q4:

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

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

Q5:

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

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

Q6:

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

  • A ( 3 , 6 ) , area = 28
  • B ( 6 , 3 ) , area = 28
  • C ( 3 , 6 ) , area = 49
  • D ( 6 , 3 ) , area = 49

Q7:

If 𝐴 𝐡 𝐢 𝐷 is a parallelogram, what can be said of the slope of line βƒ–     βƒ— 𝐴 𝐡 ?

  • Athe slope of line βƒ–     βƒ— 𝐴 𝐡 = the slope of line βƒ–     βƒ— 𝐴 𝐢
  • Bthe slope of line βƒ–     βƒ— 𝐴 𝐡 = the slope of line βƒ–     βƒ— 𝐡 𝐢
  • Cthe slope of line βƒ–     βƒ— 𝐴 𝐡 = the slope of line βƒ–      βƒ— 𝐴 𝐷
  • Dthe slope of line βƒ–     βƒ— 𝐴 𝐡 = the slope of line βƒ–     βƒ— 𝐢 𝐷

Q8:

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 𝐴 𝐡 𝐢 𝐷 . 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 𝐴 𝐡 𝐢 𝐷 .

Q9:

𝐴 𝐡 𝐢 𝐷 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 , 8 )
  • B ( 1 0 , βˆ’ 6 )
  • C ( 1 0 , 8 )
  • D ( 2 , βˆ’ 6 )

Q10:

Calculate, to two decimal places, the area of the parallelogram 𝑃 𝑄 𝑅 𝑆 , 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:

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

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

Q12:

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

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

Q13:

Suppose that and fix two sides of a parallelogram. What is the area of this parallelogram, to the nearest hundredth?

Q14:

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 𝐿 𝑀 𝑁 𝐸 to the nearest hundredth.

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