Distance and Running Problems

The video tutorial by Van explains how to use the distance formula through five examples. It starts with a basic introduction to the formula, followed by a detailed calculation of distance between two points. Alternative methods using geometric shapes are also explored. The tutorial applies the formula to real-life scenarios, such as hiking and determining distances between homes. It concludes with a comparison of joggers' paths to calculate time taken, emphasizing practical applications of the distance formula.

What is the primary purpose of the distance formula?

• To find the area of a triangle

• To determine the length of a line segment between two points

• To calculate the slope of a line

• To find the midpoint between two points

In the distance formula, what do x1, y1, x2, and y2 represent?

• The radius of a circle

• The coordinates of two points in a plane

• The angles of a triangle

• The lengths of the sides of a triangle

What is the result of applying the distance formula to the points (-9, -4) and (6, 4)?

• 21 units

• 17 units

• 19 units

• 15 units

How can you find the distance between two points if you forget the distance formula?

• By using the area formula

• By using the midpoint formula

• By drawing a right triangle and using the Pythagorean theorem

• By calculating the slope

What is the length of the line segment AB in simplest radical form if A is (-1, 3) and B is (3, -3)?

• 2√13

• 3√13

• 5√13

• 4√13

What is the total distance Katrina hikes north?

• 8 miles

• 7 miles

• 10 miles

• 5 miles

How do you calculate the straight-line distance from start to finish in Katrina's hike?

• By using the distance formula

• By applying the Pythagorean theorem

• By adding the total north and east distances

• By measuring the angles

What is the straight-line distance from start to finish in Katrina's hike, rounded to the nearest tenth?

• 9.6 miles

• 10.6 miles

• 11.6 miles

• 12.6 miles

What is the shortest distance between Jamal and Sheila's homes?

• 5.7 miles

• 6.7 miles

• 7.7 miles

• 8.7 miles

How can you find the shortest distance between two points on a grid?

• By using the midpoint formula

• By drawing a triangle and using the Pythagorean theorem

• By calculating the slope

• By using the area formula