Understanding the Distance Formula

In this tutorial, Paul explains how to use the distance formula to find the distance between two points on an XY plane. He begins by introducing the concept and then graphing the points (2,2) and (-2,-3) on the plane. Paul demonstrates how to apply the distance formula by labeling the points and substituting the values into the formula. He calculates the distance step-by-step, showing the process of squaring the differences and adding them to find the square root. The tutorial concludes with a summary of the exact and approximate distances, encouraging viewers to subscribe.

What is the primary purpose of the distance formula?

• To find the midpoint between two points

• To determine the distance between two points on an XY plane

• To calculate the slope of a line

• To find the area of a triangle

Which of the following points is correctly plotted on the XY plane?

• (2, 2) with X component 2 and Y component 3

• (-2, -3) with X component -2 and Y component -3

• (2, 2) with X component 3 and Y component 2

• (-2, -3) with X component -3 and Y component -2

When labeling points for the distance formula, which statement is true?

• X1 and Y1 must always be the first point

• X1 and Y1 must be larger than X2 and Y2

• X2 and Y2 must always be the second point

• The choice of which point is X1, Y1 or X2, Y2 does not affect the result

What is the first step in calculating the distance using the distance formula?

• Add the X components of both points

• Divide the Y1 by Y2

• Subtract the X1 from X2 and square the result

• Multiply the Y components of both points

What is the result of squaring -4 in the distance formula calculation?

• 8

• 16

• -16

• 4

What is the approximate distance between the points (2, 2) and (-2, -3)?

• 7.1

• 6.4

• 8.2

• 5.0

What is the exact distance between the points (2, 2) and (-2, -3) expressed in square root form?

• Square root of 49

• Square root of 36

• Square root of 41

• Square root of 25

What is the sum of 16 and 25 in the context of the distance formula?

• 31

• 41

• 51

• 61

What is the final step in finding the distance between two points using the distance formula?

• Take the square root of the sum of the squares

• Multiply the results of the squared differences

• Subtract the Y components

• Add the X components

What should you do if you want an exact answer for the distance between two points?

• Round the result to the nearest whole number

• Express the result in square root form

• Multiply the result by 2

• Add 10 to the result