Distance on the Coordinate Plane

This video tutorial covers how to find the distance between two points on a coordinate plane using the Pythagorean theorem and the distance formula. It includes step-by-step examples of calculating distances between points with both integer and decimal coordinates. The tutorial also explains how the distance formula is derived from the Pythagorean theorem and applies it to real-world scenarios, such as calculating distances on a map.

What theorem can be used to find the distance between two points on the coordinate plane?

• Newton's Theorem

• Archimedes' Theorem

• Pythagorean Theorem

• Euclidean Theorem

What is the distance between the points (3, 0) and (-5, -4) rounded to the nearest tenth?

• 8.4 units

• 7.8 units

• 8.9 units

• 9.1 units

Which of the following is the correct distance between the points (1, 3) and (-2, 4) rounded to the nearest tenth?

• 3.2 units

• 2.8 units

• 3.6 units

• 4.0 units

What is the distance between the points (4, 5) and (2, 2) rounded to the nearest tenth?

• 3.6 units

• 2.8 units

• 3.0 units

• 4.2 units

What is the distance formula derived from the Pythagorean theorem?

• d = √((x2 - x1)^2 + (y2 - y1)^2)

• d = (x2 - x1) + (y2 - y1)

• d = (x2 - x1)^2 + (y2 - y1)^2

• d = √((x2 + x1)^2 + (y2 + y1)^2)

Using the distance formula, what is the distance between the points (5, -4) and (-3, -2) rounded to the nearest tenth?

• 7.5 units

• 8.5 units

• 7.8 units

• 8.2 units

What is the distance between the points (-4, 2.5) and (3.5, 1) rounded to the nearest tenth?

• 5.3 units

• 5.7 units

• 6.1 units

• 4.8 units

If each unit on the grid represents 0.5 miles, what is the distance a ferry travels from (4, 12) to (6, 2) in miles?

• 5.5 miles

• 4.8 miles

• 6.0 miles

• 5.1 miles

What is the approximate distance between West Point, NY (1.5, 2) and Annapolis, MD (-1.5, -1.5) if each unit represents 45 miles?

• 200.0 miles

• 210.5 miles

• 207.4 miles

• 215.3 miles

Why does it not matter if you mix up the x and y values in the distance formula?

• Because the plus sign makes it commutative

• Because the values are squared

• All of the above

• Because the formula is symmetric