Determining Coordinates and Distances

The video tutorial explains how to find the coordinates of a point P along a directed line segment AB, where the ratio of AP to PB is 3 to 2. The instructor starts by explaining the concept of ratio in line segments and then demonstrates the calculation of the x and y coordinates of point P. The process involves determining the distance to be covered in both x and y directions and applying the given ratio to find the exact position of point P. The tutorial concludes with the final calculation, showing that point P is located at coordinates (1, 4).

What is the initial problem discussed in the video?

• Determining the coordinates of a point along a line segment

• Solving a quadratic equation

• Finding the midpoint of a line segment

• Calculating the slope of a line

What is the given ratio of AP to PB in the problem?

• 2 to 3

• 3 to 2

• 1 to 1

• 4 to 1

How is the ratio 3 to 2 interpreted in terms of distance?

• Two-fifths of the distance from A to P

• The entire distance from A to P

• Three-fifths of the distance from A to P

• Half of the distance from A to P

What is the starting x-coordinate of point A?

• 5

• 0

• -2

• 2

What is the starting y-coordinate of point A?

• -7

• 7

• 5

• 0

How much does the x-coordinate change from A to B?

• 5 units to the left

• 5 units to the right

• 7 units to the left

• 7 units to the right

How much does the y-coordinate change from A to B?

• 7 units down

• 7 units up

• 5 units down

• 5 units up

How is the horizontal distance from A to P calculated?

• By multiplying by 3/5 of the total distance

• By dividing by 3/5 of the total distance

• By adding 3/5 of the total distance

• By subtracting 3/5 of the total distance

How is the vertical distance from A to P calculated?

• By adding 3/5 of the total distance

• By subtracting 3/5 of the total distance

• By multiplying by 3/5 of the total distance

• By dividing by 3/5 of the total distance

What is the x-coordinate of point P?

• 0

• 1

• 2

• 3