Finding Distance on the Coordinate Plane with the Pythagorean Theorem

The video tutorial explains how to find the distance between two points on a coordinate plane using the Pythagorean theorem. It begins by discussing when you can count horizontal and vertical lines and when you need to use the theorem for diagonal lines. The tutorial provides several example problems, demonstrating how to draw right triangles and calculate the hypotenuse. It also covers finding the perimeter of shapes with diagonal sides and applies these concepts to a real-world scenario involving distances between attractions at Disney World.

What can be directly counted when a line is perfectly horizontal or vertical on a coordinate plane?

• The slope of the line

• The length of any diagonal line

• The length of the horizontal or vertical line

• The distance between any two points

What is the role of the legs in the Pythagorean theorem?

• They are irrelevant to finding distances

• They are the vertical and horizontal distances to be counted

• They are used to calculate the area of a triangle

• They represent the diagonal distance

What is the first step in using the Pythagorean theorem to find the distance between two points?

• Calculate the square root of the hypotenuse

• Draw a right triangle using the points as vertices

• Add the coordinates of the two points

• Count the units between the two points directly

How do you find the hypotenuse using the Pythagorean theorem?

• Subtract the squares of the legs and take the square root

• Add the squares of the legs and take the square root

• Divide the sum of the legs by two

• Multiply the lengths of the legs and take the square root

What is the distance between two points if one leg is 5 units and the other is 6 units?

• 5.5 units

• 30 units

• 7.8 units

• 11 units

What is the distance between two points if both legs are 7 units long?

• 7 units

• 14 units

• 11.4 units

• 9.9 units

How is the perimeter of a parallelogram found using the Pythagorean theorem?

• By adding the lengths of all sides directly

• By multiplying the base and height

• By calculating the diagonal distances only

• By using the theorem to find the length of diagonal sides

What is the perimeter of the parallelogram if the sides are 7, 5, 5, and 5.4 units?

• 20 units

• 22.4 units

• 17.4 units

• 24.4 units

If each unit on a map represents half a mile, what is the real-world distance between two points that are 5.1 units apart on the map?

• 2.55 miles

• 10.2 miles

• 5.1 miles

• 1.25 miles

How do you determine the number of miles represented by a distance on a map if each unit equals half a mile?

• Divide the distance in units by 2

• Multiply the distance in units by 2

• Multiply the distance in units by 0.5

• Add 0.5 to the distance in units