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1 / 10

Time

Score

Use Determinants To Find The Area Of Certain Shapes

If the vertices of a triangle in the Cartesian plane are (1, 2), (4, 5), and (6, 1), what is the area of the triangle using determinants?

5

10 How does scaling one of the vectors in a 2x2 matrix affect the area of the parallelogram it represents?

It has no effect.

It scales the area by the same factor.

True or False: The determinant of a matrix is only applicable for finding the area of rectangles.

True

False

How does the orientation of vectors affect the determinant when finding the area of a parallelogram?

It has no effect.

It changes the sign of the determinant.

True or False: The determinant method can be applied to find the area of irregular shapes with curved sides.

True

False

6 If the vertices of a quadrilateral in the Cartesian plane are (0, 0), (3, 0), (3, 2), and (0, 2), what is the area of the quadrilateral using determinants?

6

9 If the determinant of a 2x2 matrix representing the sides of a parallelogram is 0, what can be concluded about the parallelogram?

It is a square.

It has no area.

If the determinant of a matrix representing the sides of a parallelogram is 12, what is the area of the parallelogram?

6

12 If the vertices of a parallelogram in the Cartesian plane are (1, 1), (4, 1), (5, 4), and (2, 4), what is the area of the parallelogram using determinants?

9

12 If the determinant of a 2x2 matrix formed by vectors representing two sides of a parallelogram is -8, what is the area of the parallelogram?

8 -8

Questions

Time

Score

Use Determinants To Find The Area Of Certain Shapes

If the vertices of a triangle in the Cartesian plane are (1, 2), (4, 5), and (6, 1), what is the area of the triangle using determinants?

5

10

How does scaling one of the vectors in a 2x2 matrix affect the area of the parallelogram it represents?

It has no effect.

It scales the area by the same factor.

True or False: The determinant of a matrix is only applicable for finding the area of rectangles.

True

False

How does the orientation of vectors affect the determinant when finding the area of a parallelogram?

It has no effect.

It changes the sign of the determinant.

True or False: The determinant method can be applied to find the area of irregular shapes with curved sides.

True

False

6 If the vertices of a quadrilateral in the Cartesian plane are (0, 0), (3, 0), (3, 2), and (0, 2), what is the area of the quadrilateral using determinants?

6

9

If the determinant of a 2x2 matrix representing the sides of a parallelogram is 0, what can be concluded about the parallelogram?

It is a square.

It has no area.

If the determinant of a matrix representing the sides of a parallelogram is 12, what is the area of the parallelogram?

6

12

If the vertices of a parallelogram in the Cartesian plane are (1, 1), (4, 1), (5, 4), and (2, 4), what is the area of the parallelogram using determinants?

9

12

If the determinant of a 2x2 matrix formed by vectors representing two sides of a parallelogram is -8, what is the area of the parallelogram?

8

-8

Incorrect

Great!