Lesson Worksheet: Using Determinants to Calculate Areas Mathematics • 10th Grade
In this worksheet, we will practice using determinants to calculate areas of triangles and parallelograms given the coordinates of their vertices.
Q1:
Use determinants to work out the area of the triangle with vertices , , and by viewing the triangle as half of a parallelogram.
Q2:
Find the area of the triangle below using determinants.
- A18 square units
- B26 square units
- C13 square units
- D36 square units
Q3:
Use determinants to calculate the area of the parallelogram with vertices , , , and .
Q4:
Using determinants, are the points , , and collinear?
- ANo
- BYes
Q5:
Consider the quadrilateral with vertices , and .
By breaking it into two triangles as shown, calculate the area of this quadrilateral using determinants.
Q6:
Fill in the blank: If the area of a triangle whose vertices are , , and is 9 square units, then .
- A or 6
- B0 or
- C0 or 12
- D12 or
Q7:
Consider a parallelogram in which , , and are three vertices.
Complete the following: The area of this parallelogram equals square units.
Q8:
By using determinants, determine which of the following sets of points are collinear.
- A, ,
- B, ,
- C, ,
- D, ,
Q9:
If the points , , and are collinear, use determinants to find all the possible values of . Round your answers to two decimal places.
- A1.00 and 3.00
- B1.08 and
- C4.32 and
- D3.00 and
- E2.16 and
Q10:
Given the points , , , and , find the values of and if the area of the triangle is 2 square units and the points , , and are collinear.
- A or and
- B or and
- C or 5 and
- D or 5 and
- E and
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