Coordinate Geometry Proofs Challenge

The video tutorial introduces coordinate geometry proofs, focusing on proving a quadrilateral is a rectangle and not a square. It covers plotting points, calculating slopes and distances, and proving perpendicularity. The tutorial concludes with a practice problem to reinforce learning.

What is the first step in a coordinate geometry proof?

• Calculate the slopes of the sides

• Determine the angles

• Find the midpoints

• Plot the points

How do you calculate the slope between two points?

• y1 - y2 / x1 - x2

• x1 - x2 / y1 - y2

• y2 - y1 / x2 - x1

• x2 - x1 / y2 - y1

What is the slope of the line segment AB if A is (-3, -2) and B is (-1, 2)?

• -1/2

• 2

• -2

• 1/2

What is the slope of the line segment CD if C is (1, 1) and D is (-1, -3)?

• -1/2

• 1/2

• -2

• 2

What is the formula for calculating the distance between two points?

• sqrt((x1 - x2)^2 + (y1 - y2)^2)

• sqrt((x1 - x2) + (y1 - y2))

• sqrt((x2 - x1)^2 + (y2 - y1)^2)

• sqrt((x2 - x1) + (y2 - y1))

What is the distance between points A (-3, -2) and B (-1, 2)?

• sqrt(5)

• sqrt(10)

• sqrt(20)

• sqrt(25)

What is the distance between points C (1, 1) and D (-1, -3)?

• sqrt(10)

• sqrt(20)

• sqrt(5)

• sqrt(25)

What is the key difference between a rectangle and a square in terms of side lengths?

• Opposite sides are equal in a square

• Adjacent sides are equal in a rectangle

• All sides are equal in a square

• All sides are equal in a rectangle

What must be true about the slopes of consecutive sides of a rectangle?

• They must be positive reciprocals

• They must be negative reciprocals

• They must be zero

• They must be equal

Why is quadrilateral ABCD not a square?

• Opposite sides are not equal

• Diagonals are not equal

• All angles are not right angles

• All sides are not equal