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Questions and Answers
What is distance referred to as in certain problems?
What is required to calculate the distance using the coordinate plane?
What do the subscripts 1 and 2 represent in the distance equation?
What is another way to calculate distance?
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What is needed to determine how much gas you may need for a trip?
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What is the difference between the distance equation used in two-dimensional and three-dimensional problems?
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What is the purpose of using the distance rate time formula?
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What is the condition for using the distance rate time formula?
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How can you use the distance formula to determine the rate of travel?
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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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Description
Learn about calculating distance using the rate and time formula and the coordinate plane formula, and understand the concept of coordinates in the coordinate plane.
