Distance on the Coordinate Plane Explained

What is the essential question discussed in the introduction?

• How to calculate the area of a triangle on the coordinate plane.

• How to use the Pythagorean theorem to find the distance between two points on the coordinate plane.

• How to find the midpoint between two points on the coordinate plane.

• How to determine the slope of a line on the coordinate plane.

Which two mathematical concepts are combined to form the distance formula?

• Area formula and Pythagorean theorem

• Slope formula and Pythagorean theorem

• Slope formula and midpoint formula

• Midpoint formula and Pythagorean theorem

In the distance formula, what does 'c' represent?

• The slope of the line

• The y-coordinate of the second point

• The x-coordinate of the first point

• The distance between two points

What is the distance formula derived from the Pythagorean theorem and slope formula?

• d = √((x2 - x1) + (y2 - y1))

• d = (x2 - x1) / (y2 - y1)

• d = (x2 - x1) + (y2 - y1)

• d = √((x2 - x1)^2 + (y2 - y1)^2)

In Example 1, what is the distance between the points (3, 0) and (7, -5)?

• 7.2 units

• 8.1 units

• 6.4 units

• 5.0 units

What is the first step in using the distance formula?

• Add the coordinates together

• Multiply the coordinates

• Square the differences of the coordinates

• Subtract the y-coordinates and x-coordinates

In Example 2, what is the approximate distance between West Point and Annapolis on the map?

• 4.6 units

• 3.5 units

• 6.1 units

• 5.2 units

How do you convert the map distance to real-world distance in Example 2?

• Divide the map distance by the number of miles per unit

• Multiply the map distance by the number of miles per unit

• Add the map distance to the number of miles per unit

• Subtract the map distance from the number of miles per unit

In the practice problem, what is the distance between the points (1, 5) and (3, 1)?

• 5.0 units

• 4.5 units

• 4.0 units

• 3.6 units

In the second practice problem, if each unit on the map equals 16.5 miles, what is the approximate distance between Mankato and Duluth?

• 350 miles

• 300 miles

• 250 miles

• 200 miles