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.

**Q2: **

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

- A , trapezium
- B , parallelogram
- C , trapezium
- D , parallelogram

**Q3: **

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

- A , area = 24
- B , area = 24
- C , area = 35
- D , area = 35

**Q4: **

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

- Athe slope of line = the slope of line
- Bthe slope of line = the slope of line
- Cthe slope of line = the slope of line
- Dthe slope of line = the slope of line

**Q5: **

is a parallelogram. The coordinates of the points , , and are , , and respectively. Find the coordinates of .

- A
- B
- C
- D

**Q6: **

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

**Q7: **

Given that , , and , determine the area of the parallelogram to the nearest hundredth.

**Q8: **

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

**Q9: **

A parallelogram has vertices at the points , , , and with coordinates , , , and respectively.

Work out the perimeter of the parallelogram . 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 .

**Q10: **

Calculate, to two decimal places, the area of the parallelogram , where the coordinates of its vertices are at , , , and .

**Q12: **

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

- A , area = 24
- B , area = 24
- C , area = 36
- D , area = 36

**Q13: **

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

- A , area = 28
- B , area = 28
- C , area = 49
- D , area = 49

**Q14: **

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

- A , trapezium
- B , parallelogram
- C , trapezium
- D , parallelogram