Exploring Distance and Midpoint in Geometry

This video tutorial covers the distance and midpoint formulas on both a number line and a coordinate plane. It begins with an introduction to the concepts, emphasizing that distance is always positive. The video then provides detailed examples of calculating distance and midpoint on a number line, using absolute values and averages. It transitions to the coordinate plane, explaining how to apply the distance and midpoint formulas to ordered pairs. The tutorial concludes with advanced problems, including finding missing endpoints and solving polynomial equations, reinforcing the concepts with practical examples.

What is always true about the distance between any two points?

• It can be negative.

• It is always positive.

• It depends on the direction.

• It can be zero.

How do you find the distance between two points on a number line?

• By multiplying the two points.

• By taking the absolute value of the difference between the two points.

• By subtracting the smaller point from the larger point.

• By adding the two points.

What is the midpoint formula on a number line?

• a - b

• a + b / 2

• a + b

• a + b / 2

If the points are -2 and 2 on a number line, what is the midpoint?

• 0

• 1

• 2

• -2

What is the distance formula on the coordinate plane?

• sqrt((x2 + x1) + (y2 + y1))

• sqrt((x2 - x1)^2 + (y2 - y1)^2)

• sqrt((x2 + x1)^2 + (y2 + y1)^2)

• sqrt((x2 - x1) + (y2 - y1))

How do you find the midpoint on the coordinate plane?

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

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

• Divide the x-coordinates and y-coordinates separately by 2.

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

What is the distance between points A(4, 6) and B(-8, 4)?

• sqrt(225)

• sqrt(245)

• sqrt(169)

• sqrt(148)

What is the midpoint between points A(4, 6) and B(-8, 4)?

• (-2, 5)

• (2, -5)

• (5, -2)

• (-5, 2)

If C is the midpoint of AB, and A is (5, 4) and C is (6, 3), what is the coordinate of B?

• (7, 4)

• (7, 3)

• (7, 5)

• (7, 2)

What is the y-coordinate if the distance between (5, 9) and (-7, y) is 15 units?

• 0 or 18

• 0 or -18

• 18 or -18

• 9 or -9