Distance Formula and Its Applications

The video tutorial introduces the distance formula, focusing first on a graphical approach using the Pythagorean theorem to find the distance between two points. It explains how to form a right triangle and use the theorem to calculate the hypotenuse, which represents the distance. The tutorial then shifts to an algebraic approach, demonstrating how to use the distance formula with coordinate pairs. The video concludes with a summary of both methods and emphasizes the importance of positive distance values.

What is the first step in finding the distance between two points graphically?

• Draw a circle around the points

• Draw a line connecting the points

• Draw a square around the points

• Draw a right triangle using the points

Which theorem is used to calculate the distance between two points on a graph?

• Remainder theorem

• Fundamental theorem of calculus

• Pythagorean theorem

• Binomial theorem

What is the length of the hypotenuse if the sides of the triangle are 3 and 4 units?

• 6 units

• 5 units

• 7 units

• 8 units

What is the purpose of the distance formula?

• To find the midpoint between two points

• To find the area of a triangle

• To calculate the slope of a line

• To determine the distance between two points

How do you label the coordinates when using the distance formula?

• P1, Q1 and P2, Q2

• M1, N1 and M2, N2

• X1, Y1 and X2, Y2

• A1, B1 and A2, B2

What is the result of subtracting the y-coordinates in the distance formula?

• The length of the hypotenuse

• The difference in x-coordinates

• The difference in y-coordinates

• The sum of the coordinates

Why is the distance always considered positive?

• Because it is a direction

• Because it represents a length

• Because it is a vector quantity

• Because it is a scalar quantity

What is the algebraic expression for the distance formula?

• d = (X2 - X1) + (Y2 - Y1)

• d = (X2 + X1)^2 + (Y2 + Y1)^2

• d = √((X2 - X1)^2 + (Y2 - Y1)^2)

• d = (X2 - X1)^2 - (Y2 - Y1)^2

What is the graphical approach to finding the distance between two points?

• Using a protractor

• Using a compass

• Using a ruler

• Using a right triangle

What is the final step in using the distance formula?

• Subtract the coordinates

• Add the coordinates

• Take the square root of the sum

• Square the differences and add them