Midpoint and Distance Formulas

This video tutorial covers the midpoint and distance formulas in geometry. It begins with an introduction to the concepts, followed by a detailed explanation of the midpoint formula, including examples. The tutorial then explores how to partition a segment in a given ratio, providing step-by-step instructions. Finally, the distance formula is explained with an example to illustrate its application.

What is the main focus of this geometry lesson?

• Learning about midpoint and distance formulas

• Studying the Pythagorean theorem

• Understanding angles and their properties

• Exploring the properties of triangles

What does the midpoint formula help you find?

• The angle between two lines

• The length of a line segment

• The area of a triangle

• The point that divides a segment into two equal parts

How do you calculate the midpoint of a segment with endpoints (-1, -1) and (-5, -5)?

• (-3, -3)

• (-4, -4)

• (-6, -6)

• (-2, -2)

What is the midpoint of the segment with endpoints (2, -5) and (-5, 5)?

• (-2, 0)

• (-0.5, 0)

• (-3, 0)

• (-1.5, 0)

What is the goal when finding a partition of a segment?

• To find a point that is a specific fraction of the way between two endpoints

• To calculate the length of the segment

• To find the midpoint of the segment

• To determine the slope of the segment

How do you calculate the horizontal distance for a partition?

• By adding the x-values of the endpoints

• By dividing the x-values by the desired fraction

• By finding the average of the x-values

• By subtracting the x-values and multiplying by the desired fraction

What is the point that is three-fifths of the way from A(3, -4) to B(13, 11)?

• (7, 3)

• (10, 6)

• (8, 4)

• (9, 5)

What is the first step in finding a partition of a segment?

• Add the coordinates of the endpoints

• Calculate the midpoint

• Find the horizontal distance and multiply by the fraction

• Determine the slope of the segment

What does the distance formula calculate?

• The area of a triangle

• The slope of a line

• The length of a segment between two points

• The midpoint of a segment

Using the distance formula, what is the distance between the points (5, 9) and (-7, -7)?

• 10 units

• 20 units

• 25 units

• 15 units