Coordinate Plane and Distance Equation
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Questions and Answers

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?

  • 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?

  • 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?

    <p>Using the rate and time</p> Signup and view all the answers

    What is needed to determine how much gas you may need for a trip?

    <p>The distance between two points</p> Signup and view all the answers

    What is the difference between the distance equation used in two-dimensional and three-dimensional problems?

    <p>The formula used in three-dimensional problems has an additional variable for the z-axis</p> Signup and view all the answers

    What is the purpose of using the distance rate time formula?

    <p>To calculate the distance traveled in a given time period</p> Signup and view all the answers

    What is the condition for using the distance rate time formula?

    <p>The rate and time must have the same units of measure</p> Signup and view all the answers

    How can you use the distance formula to determine the rate of travel?

    <p>By rearranging the formula to isolate the rate</p> Signup and view all the answers

    What is the purpose of rearranging the distance formula to find the time?

    <p>To determine the time it will take to travel a certain distance</p> Signup and view all the answers

    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.

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