Understanding Ratios and Distances on a Line Segment

The video tutorial explains how to find a point B on a line segment AC such that the ratio of AB to BC is 3:1. It involves understanding the problem, breaking it down into horizontal and vertical components, and calculating the distances to determine the coordinates of point B. The tutorial uses concepts of geometry, ratios, and distance calculations to solve the problem.

What is the main objective of the problem discussed in the video?

• To calculate the length of segment AC

• To determine the slope of line AC

• To find the midpoint of segment AC

• To find point B such that AB to BC is 3 to 1

How is the ratio of AB to BC expressed mathematically?

• As 4x to x

• As 2:1

• As 3x to x

• As 1:3

What is the total distance of segment AC if AB is 3x and BC is x?

• 3x

• 2x

• 4x

• 5x

How is the position of point B determined along segment AC?

• By finding the midpoint

• By calculating 1/3 of the distance

• By calculating 1/4 of the distance

• By using the distance formula

What is the horizontal change between points A and C?

• 8 units

• 12 units

• 4 units

• 16 units

What is the vertical change between points A and C?

• 2 units

• 3 units

• 4 units

• 5 units

How far vertically do you move from point C to reach point B?

• 1 unit

• 3 units

• 2 units

• 4 units

How far horizontally do you move from point C to reach point B?

• 2 units

• 5 units

• 3 units

• 4 units

What are the coordinates of point B?

• (-3, 2)

• (-2, 3)

• (3, -2)

• (2, -3)

What is the relationship between the distances CB and BA?

• CB is one-third of BA

• CB is equal to BA

• CB is half of BA

• CB is twice BA