Understanding Distance in Coordinate Plane

The video tutorial explains how to calculate the distance between two points on a coordinate plane using the Pythagorean theorem. It begins with an introduction to the concept, followed by a detailed example of finding the distance between two points. The tutorial then explains the distance formula, showing its derivation from the Pythagorean theorem. Finally, another example is provided to reinforce the concept, concluding with a summary of the key points.

What is the main mathematical concept used to find the distance between two points in a coordinate plane?

• Pythagorean theorem

• Quadratic formula

• Binomial theorem

• Law of sines

In the example with points (3, -4) and (6, 0), what is the change in the x-coordinate?

• 0

• 9

• 6

• 3

How do you calculate the change in y for the points (3, -4) and (6, 0)?

• 0 - (-4)

• 6 - 3

• 3 - 6

• 4 - 0

What is the distance between the points (3, -4) and (6, 0) using the Pythagorean theorem?

• 6 units

• 3 units

• 4 units

• 5 units

What is the formula for the distance between two points (x1, y1) and (x2, y2)?

• √((x2 + x1)² + (y2 + y1)²)

• (x2 - x1) + (y2 - y1)

• √((x2 - x1)² + (y2 - y1)²)

• (x2 + x1)² + (y2 + y1)²

Why is it unnecessary to memorize the distance formula?

• It changes based on the coordinate system.

• It is too complex to remember.

• It is derived from the Pythagorean theorem.

• It is not used in real-world applications.

In the second example, what is the change in x between the points (-6, -4) and (1, 7)?

• 5

• 13

• 11

• 7

What is the change in y for the points (-6, -4) and (1, 7)?

• 5

• 13

• 7

• 11

What is the calculated distance between the points (-6, -4) and (1, 7)?

• 5 units

• 11 units

• 13.04 units

• 7 units

Which theorem is used to derive the distance formula?

• Fundamental theorem of calculus

• Binomial theorem

• Pythagorean theorem

• Law of cosines