Exploring Area and Perimeter in Coordinate Geometry

What formula is used to calculate the distance between two points in the coordinate plane?

• Quadratic formula

• Pythagorean theorem

• Distance formula

• Slope formula

What property do perpendicular lines have regarding their slopes?

• Their slopes are equal

• Their slopes are opposite reciprocals

• Their slopes are both positive

• Their slopes are both negative

How do you verify that a shape is a rectangle using slopes?

• Check if opposite sides are parallel

• Check if all angles are 90 degrees

• Check if all sides are equal

• Check if adjacent sides are perpendicular

What is the area of a rectangle if the base is 2√5 and the height is 3√5?

• 15 units squared

• 30 units squared

• 25 units squared

• 10 units squared

What method is used to find the area of a complex polygon in the coordinate plane?

• Using the distance formula on all sides

• Adding the area of all internal triangles

• Calculating the perimeter and dividing by the number of sides

• Subtracting the area of internal shapes from the total area

How many units squared is the area of the large square used to calculate the area of the trapezoid-like polygon?

• 56 units squared

• 60 units squared

• 50 units squared

• 45 units squared

What is the area of triangle A within the large square?

• 10 units squared

• 20 units squared

• 5 units squared

• 15 units squared

What is the area of triangle D within the large square?

• 3 units squared

• 5 units squared

• 7 units squared

• 9 units squared

What is the corrected total area of the trapezoid-like polygon after subtracting the areas of the triangles?

• 29 units squared

• 25 units squared

• 31 units squared

• 35 units squared

What is the final step in the method used to find the area of the trapezoid-like polygon?

• Add the areas of the triangles

• Divide the area of the large square by the number of triangles

• Multiply the base and height of the large square

• Subtract the areas of the triangles from the area of the large square