Coordinate Geometry: Proving a Rectangle

The video tutorial demonstrates how to prove a quadrilateral is a rectangle using coordinate geometry. It explains the importance of showing that all angles are right angles by proving the sides are perpendicular. The process involves graphing points, calculating slopes, and verifying that opposite slopes are reciprocals. The tutorial concludes by emphasizing the need to write complete sentences when explaining the proof.

What is the primary method used to prove a rectangle in coordinate geometry?

• Showing all sides are equal

• Showing all sides are parallel

• Showing all angles are right angles

• Showing all diagonals are equal

How do you determine if two sides are perpendicular in coordinate geometry?

• By checking if their lengths are equal

• By checking if their slopes are equal

• By checking if their slopes are opposite reciprocals

• By checking if their angles are equal

What is the slope of a line segment with endpoints (4, 7) and (9, 2)?

• 2

• -1

• 0

• 1

Why should you avoid calculating the slope of diagonals when proving a rectangle?

• Because diagonals are not perpendicular

• Because diagonals are always equal

• Because diagonals are not sides of the rectangle

• Because diagonals do not affect the angles

What indicates that two slopes are opposite reciprocals?

• Their sum is zero

• One is positive and the other is negative, and their product is -1

• They are both negative

• They are both positive

If the slope of one side is 1, what should be the slope of the perpendicular side?

• -1

• 2

• 1

• 0

What is the significance of having two pairs of opposite reciprocal slopes in a quadrilateral?

• It confirms the quadrilateral is a parallelogram

• It confirms the quadrilateral is a rectangle

• It confirms the quadrilateral is a square

• It confirms the quadrilateral is a rhombus

What should you include in your explanation when stating that two lines are perpendicular?

• The fact that their slopes are opposite reciprocals

• The coordinates of the endpoints

• The lengths of the lines

• The angles between the lines

What is the result of flipping the fraction 1/1?

• 1/1

• -1

• 0

• 2

Why is it important to write a sentence explaining perpendicularity in a proof?

• To avoid using mathematical terms

• To confuse the reader

• To ensure clarity and understanding

• To make the proof longer