Classifying Quadrilaterals in the Coordinate Plane

The video tutorial explains how to classify quadrilaterals in the coordinate plane using mathematical proofs. It covers the use of the distance formula to determine segment lengths and congruence, and the comparison of slopes to check for perpendicularity. The tutorial also discusses analyzing diagonals for congruence to differentiate between rectangles and other quadrilaterals. The process is demonstrated with a specific example, leading to the conclusion that the given quadrilateral is a rectangle.

What are the four types of quadrilaterals mentioned in the video?

• Parallelogram, Rhombus, Square, Rectangle

• Triangle, Circle, Square, Rectangle

• Hexagon, Pentagon, Square, Rectangle

• Parallelogram, Triangle, Square, Rectangle

What is the purpose of using the distance formula in classifying quadrilaterals?

• To calculate the perimeter of the quadrilateral

• To find the angles of the quadrilateral

• To determine if the sides are congruent

• To find the area of the quadrilateral

Which formula is used to find the length of a segment between two points?

• Slope formula

• Midpoint formula

• Area formula

• Distance formula

What does it mean if the slopes of two sides are perpendicular?

• The sides are congruent

• The sides form a right angle

• The sides are equal in length

• The sides are parallel

How do you determine if two sides are parallel using slopes?

• Their slopes are equal

• Their slopes are negative reciprocals

• Their slopes are both positive

• Their slopes add up to zero

What is the length of segment AB if the coordinates are A(9, -4) and B(8, -2)?

• √5

• √10

• √2

• √13

What is the simplified form of the square root of 45?

• 5√3

• 3√5

• √9

• 9√5

If the slope of AB is -2, what is the slope of a line perpendicular to AB?

• -2

• -1/2

• 2

• 1/2

What is the slope of segment CD if the coordinates are C(2, -5) and D(3, -7)?

• -1/2

• 1/2

• -2

• 2

Based on the segment lengths and slopes, what is the final classification of the quadrilateral?

• Rectangle

• Parallelogram

• Rhombus

• Square