Finding Distances Between Points on a Plane Using the Pythagorean Theorem

The video tutorial explains how to calculate the distance between two points on a plane using the Pythagorean theorem. It begins with a review of the theorem, then demonstrates how to apply it to find the distance between specific points by forming a right triangle. The tutorial further derives a general distance formula using variables, allowing for easy calculation without drawing triangles. The formula is tested with example points to confirm its accuracy.

What does the Pythagorean theorem relate in a right triangle?

• The angles and the hypotenuse

• The legs and the hypotenuse

• The perimeter and the area

• The base and the height

How do you determine the third vertex when creating a right triangle from two points?

• By using the slope of the line

• By averaging the coordinates of the two points

• By aligning vertically and horizontally with the given points

• By using the midpoint formula

What is the vertical distance between the points (2, 4) and (2, -1)?

• 3 units

• 4 units

• 6 units

• 5 units

What is the result of applying the Pythagorean theorem to the points (2, 4) and (-4, -1)?

• The distance is 12

• The distance is 7

• The distance is the square root of 61

• The distance is 10

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

• y1 - y2

• y1 + y2

• x1 - x2

• x1 + x2

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

• d = sqrt((x1 + x2)^2 + (y1 + y2)^2)

• d = sqrt((x1 - x2)^2 + (y1 - y2)^2)

• d = (x1 - x2)^2 + (y1 - y2)^2

• d = (x1 + x2)^2 + (y1 + y2)^2

How can the distance formula be used to find the distance between two points without drawing a triangle?

• By using the midpoint formula

• By substituting the coordinates into the formula

• By using the area of the triangle

• By calculating the slope