Exploring Area and Perimeter of Triangles in the Coordinate Plane

What formula is used to calculate the length of each side of a triangle?

• Pythagorean theorem

• Distance formula

• Area formula

• Circumference formula

What is the result of applying the distance formula to side OA?

• Square root of 29

• Square root of 25

• 2 radical 2

• 5

What is the first step in the 'boxing in' method for finding a triangle's area?

• Calculate the area of the triangle directly

• Subtract the area of extraneous triangles

• Enclose the triangle within a rectangle

• Find the height of the triangle

How is the area of the rectangle used in the 'boxing in' method?

• It is used to calculate the triangle's perimeter

• Extraneous triangle areas are subtracted from it

• It is multiplied by the height of the triangle

• It is divided by 2

What is the area of triangle 3 in the 'boxing in' method example?

• 2 square units

• 5 square units

• 7 square units

• 11 square units

What does the general area formula for a triangle allow you to calculate?

• The area of a triangle with a vertex at the origin

• The height of any triangle

• The perimeter of any triangle

• The volume of a triangular prism

What is the simplified result of the general area formula for the example given?

• 5 square units

• 1.5 square units

• 7 square units

• 11 square units

How do you adapt the general area formula for a triangle not positioned with a vertex at the origin?

• Multiply each coordinate by 2

• Use the Pythagorean theorem

• Apply a translation to move a vertex to the origin

• No adaptation is necessary

What is the purpose of applying a translation to a triangle before using the general area formula?

• To change the triangle's orientation

• To position a vertex at the origin

• To simplify the calculation of the perimeter

• To increase the area of the triangle

After applying the translation vector, what are the coordinates of A'?

• 2, 1

• 1, 2

• 0, 0

• 3, 4