Podcast
Questions and Answers
What is distance referred to as in certain problems?
What is distance referred to as in certain problems?
- Length or width
- Height or how far
- Length, width, or height
- All of the above (correct)
What is required to calculate the distance using the coordinate plane?
What is required to calculate the distance using the coordinate plane?
- The rate and time
- The length and width of the coordinate plane
- The (x, y) coordinate pair for two points (correct)
- The distance formula
What do the subscripts 1 and 2 represent in the distance equation?
What do the subscripts 1 and 2 represent in the distance equation?
- The coordinates of the two points
- The x and y values
- The first and second points (correct)
- The rate and time
What is another way to calculate distance?
What is another way to calculate distance?
What is needed to determine how much gas you may need for a trip?
What is needed to determine how much gas you may need for a trip?
What is the difference between the distance equation used in two-dimensional and three-dimensional problems?
What is the difference between the distance equation used in two-dimensional and three-dimensional problems?
What is the purpose of using the distance rate time formula?
What is the purpose of using the distance rate time formula?
What is the condition for using the distance rate time formula?
What is the condition for using the distance rate time formula?
How can you use the distance formula to determine the rate of travel?
How can you use the distance formula to determine the rate of travel?
What is the purpose of rearranging the distance formula to find the time?
What is the purpose of rearranging the distance formula to find the time?
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Study Notes
Distance and Coordinate Plane
- Distance refers to the length between two points or objects, often used in real-world problems to calculate quantities like gas consumption or paint needed.
- Distance can be calculated using the rate and time formula (d = rt) or the coordinate plane formula.
Coordinate Plane and Distance Equation
- A coordinate provides a location of a point in the coordinate plane, written as (x, y).
- The distance equation (formula) is d = √((x2 - x1)^2 + (y2 - y1)^2), used to calculate the distance between two points in a two-dimensional plane.
Three-Dimensional Plane
- In three-dimensional problems, the distance equation becomes d = √((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2).
Distance Rate Time Formula
- The distance rate time formula is d = rt, where d is the distance, r is the rate, and t is the time.
- Ensure the same units of measure are used for the rate and time.
Distance Formula Examples
- Example 1: Calculate the distance between two points in a coordinate plane, resulting in approximately 5 units.
- Example 2: Calculate the distance between two points in a three-dimensional plane, resulting in approximately 5 units.
Word Problems
- Example 3: Calculate the distance traveled in a certain time at a given rate, resulting in approximately 15 miles.
- Example 4: Calculate the total distance traveled on a certain amount of gas, resulting in approximately 210 miles.
Solving Distance Rate and Time Problems
- The distance formula can be rearranged to find rate and time.
- To find miles per hour, rearrange the formula to isolate r, resulting in r = d / t.
- To calculate time, rearrange the formula to isolate t, resulting in t = d / r.
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