Distance and Midpoint Formulas

The video tutorial covers key concepts in coordinate geometry, including how to find the distance between two points using the distance formula derived from Pythagoras' theorem. It also explains how to calculate the gradient, which measures the steepness between points. The tutorial then focuses on finding the midpoint between two points, using examples to illustrate the process and verify calculations. The teacher emphasizes understanding the underlying principles and provides practical examples to reinforce learning.

What is the formula used to calculate the distance between two points in coordinate geometry?

• Area formula

• Distance formula

• Midpoint formula

• Gradient formula

Which theorem is the distance formula derived from?

• Euclid's theorem

• Pythagoras' theorem

• Archimedes' theorem

• Newton's theorem

What does the gradient formula help determine between two points?

• The distance between them

• The midpoint between them

• The area between them

• The steepness between them

What are the components of the gradient formula?

• Rise and fall

• Rise and run

• Run and walk

• Walk and rise

What is the midpoint of a line segment?

• The point at the end of the segment

• The point exactly halfway between the endpoints

• The point outside the segment

• The point at the start of the segment

How do you calculate the x-coordinate of the midpoint between two points?

• Add the x-coordinates and multiply by two

• Multiply the x-coordinates and add two

• Subtract the x-coordinates and divide by two

• Add the x-coordinates and divide by two

In the example, what was the x-coordinate of the midpoint between points A and P?

• 3

• 4

• 5

• 6

What is the y-coordinate of the midpoint between two points on the same horizontal line?

• The average of the y-coordinates

• The same as the y-coordinate of the points

• The difference of the y-coordinates

• The sum of the y-coordinates

In the vertical line example, what was the x-coordinate of the midpoint between points B and P?

• 7

• 5

• 6

• 8

Why is the method of finding the midpoint considered versatile?

• It only works for horizontal lines

• It can be applied to any two points regardless of their position

• It is only applicable to points on the x-axis

• It only works for vertical lines