Math Problem Statement
The class of math is mapped on a coordinate grade with the origin being the center of the point of the hall. Mary C is located at the point -4, seven and Betty C is located at -2, five how far is it from Mary seat to Betty seat.
Solution
To find the distance between Mary C's seat at and Betty C's seat at , we use the distance formula for two points and :
Step-by-step calculation:
- Let be Mary's location , and be Betty's location .
- Calculate the differences in coordinates:
- Substitute into the distance formula:
- Simplify:
Thus, the distance between Mary C's and Betty C's seats is approximately units.
Do you have any questions or want more details?
Follow-up Questions:
- How would you visualize this distance on a coordinate plane?
- What are other methods to calculate the distance between points?
- How does the distance formula change for three-dimensional space?
- Can we calculate the slope of the line connecting these two points?
- If the seats were aligned horizontally or vertically, how would the distance formula simplify?
Tip: The distance formula is an application of the Pythagorean Theorem and works for any two points on a plane.
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Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Distance Formula
Cartesian Coordinates
Formulas
Distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Theorems
Pythagorean Theorem (as basis for distance formula)
Suitable Grade Level
Grades 6-8