Mastering 9-0 Notes on Rational Expressions

Mrs. Johnson covers the distance and midpoint formulas, explaining their derivations and applications. She connects these concepts to the Pythagorean theorem and discusses their role in bridging geometry and algebra. The video includes practical examples, such as finding the distance between points and determining the other endpoint given a midpoint. Completing the square is revisited, emphasizing its use in converting equations to vertex form. Finally, the video explains how to find the equation of a perpendicular bisector, highlighting the importance of slope and midpoint calculations.

What does the distance formula calculate?

• The area of a triangle

• The midpoint between two points

• The slope of a line

• The distance between two points

Which theorem is the distance formula derived from?

• Pythagorean theorem

• Slope-intercept theorem

• Midpoint theorem

• Quadratic theorem

What does the midpoint formula calculate?

• The slope of a line

• The midpoint between two points

• The area of a rectangle

• The distance between two points

How do you find the midpoint between two points?

• Multiply the x-coordinates and y-coordinates, then divide by 2

• Subtract the x-coordinates and y-coordinates, then divide by 2

• Divide the x-coordinates and y-coordinates, then add 2

• Add the x-coordinates and y-coordinates, then divide by 2

What is the distance between the points (-2, -1) and (-4, 3)?

• √20

• 4

• 2√5

• 5

What is the midpoint of the points (-2, -1) and (-4, 3)?

• (-3, -1)

• (0, 0)

• (-1, 2)

• (-3, 1)

What is the first step in completing the square for the equation 3x^2 - 18x + 5 = 0?

• Multiply everything by 3

• Add 5 to both sides

• Divide everything by 3

• Subtract 5 from both sides

What is the result of completing the square for the equation x^2 - 6x = 9?

• (x - 3)^2 = 15

• (x + 3)^2 = 15

• (x - 3)^2 = 9

• (x + 3)^2 = 9

What does it mean for a line to be perpendicular to another line?

• It has the same slope

• It intersects at a 45-degree angle

• It intersects at a 90-degree angle

• It is parallel to the other line

What is the slope of a line perpendicular to a line with slope -4/3?

• 4/3

• -3/4

• 3/4

• -4/3