Coordinate Geometry Concepts and Formulas

This video tutorial covers coordinate proofs in geometry, focusing on proving a quadrilateral is a parallelogram. It introduces five methods: showing both pairs of opposite sides are parallel, diagonals bisect each other, one pair of opposite sides is parallel and congruent, both pairs of opposite sides are congruent, and both pairs of opposite angles are congruent. The video demonstrates four of these methods using the slope, midpoint, and distance formulas, providing step-by-step examples and calculations.

What is the main topic discussed in the video?

• Calculus derivatives

• Coordinate proofs in geometry

• Algebraic equations

• Trigonometric identities

How many methods are there to prove a quadrilateral is a parallelogram?

• Five

• Four

• Six

• Three

Which formula is used to show that both pairs of opposite sides are parallel?

• Area formula

• Distance formula

• Midpoint formula

• Slope formula

What does it mean if two lines have the same slope?

• They intersect

• They are parallel

• They are congruent

• They are perpendicular

What is the slope of line AD if the coordinates are A(1, 2) and D(-1, -1)?

• 2/3

• 2

• 3/2

• 1/2

Which formula is used to prove that diagonals bisect each other?

• Distance formula

• Area formula

• Slope formula

• Midpoint formula

What is the midpoint of AC if A(1, 2) and C(0, -5)?

• (0.5, -1.5)

• (1, -3)

• (0, -1)

• (0.5, -3.5)

Which formula is used to show one pair of opposite sides is both parallel and congruent?

• Area formula

• Distance formula

• Midpoint formula

• Slope formula

What is the length of AD if A(1, 2) and D(-1, -1)?

• √20

• √17

• √10

• √13

Which formula is used to prove both pairs of opposite sides are congruent?

• Slope formula

• Midpoint formula

• Distance formula

• Area formula